MATH 221 Statistics for Decision Making

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MATH 221 Statistics for Decision Making
Statistical Concepts that you will learn after completing this iLab…

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MATH 221 Statistics for Decision Making

MATH 221 Statistics for Decision Making

MATH 221 Statistics for Decision-Making

https://www.hiqualitytutorials.com/product/statistics-for-decision-making/

A+ iLab Week 2, 4, 6| Homework Week 1-7| Quiz Week 3, 5, 7| Discussions Week 1-7 |Final Exam

Week 3 Quiz – 3 Sets

Week 5 Quiz – 3 Sets

Week 7 Quiz 4 Sets

All Quizzes and Final Exam Include Formulas in Excel and in Word that can be used if a numerical data is different  ALL 100% Correct.

Statistics for Decision Making

iLab Week 2 

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Statistical Concepts that you will learn after completing this iLab:

  • Using Excel for Statistics
  • Graphics
  • Shapes of Distributions
  • Descriptive Statistics
  • Empirical Rule

Week 2 iLab Instructions-BEGIN

  • Data have already been formatted and entered into an Excel worksheet.
  • Obtain the data file for this lab from your instructor.
  • The names of each variable from the survey are in the first row of the Worksheet. This row has a background color of gray to identify it as the variable names. All other rows of the Worksheet represent a certain students’ answers to the survey questions. Therefore, the rows are called observations and the columns are called variables. On page 6 of this lab, you will find a code sheet that identifies the correspondence between the variable names and the survey questions.
  • Follow the directions below and then paste the graphs from Excel in the grey areas for question 1 through 3. Type your answers to questions 4 through 11 where noted in the grey areas. When asked for explanations, please give thorough, multi-sentence or paragraph length explanations.
  • PLEASE NOTE that various versions of Excel may have slightly different formula commands. For example, some versions use =STDEV.S while other versions would use =STDEVS (without the dot before the last “S”).
  • The completed iLab Word Document with your responses to the 11 questions will be the ONE and only document submitted to the dropbox. When saving and submitting the document, you are required to use the following format: Last Name_ First Name_Week2iLab.

Week 2 iLab Instructions-END

Creating Graphs

Create a pie chart for the variable Car Color: Select the column with the Car variable, including the title of Car Color.  Click on Insert, and then Recommended Charts.  It should show a clustered column and click OK.  Once the chart is shown, right click on the chart (main area) and select Change Chart Type.  Select Pie and OK.  Click on the pie slices, right click Add Data Labels, and select Add Data Callouts.  Add an appropriate title.  Copy and paste the chart here. (4 points)

Create a histogram for the variable Height. You need to create a frequency distribution for the data by hand.  Use 5 classes, find the class width, and then create the classes.  Once you have the classes, count how many data points fall within each class. It may be helpful to sort the data based on the Height variable first.  Create a new worksheet in Excel by clicking on the + along the bottom of the screen and type in the categories and the frequency for each category.  Then select the frequency table, click on Insert, then Recommended Charts and choose the column chart shown and click OK.  Right click on one of the bars and select Format Data Series.  In the pop up box, change the Gap Width to 0.  Add an appropriate title and axis label.  Copy and paste the graph here. (4 points)

  1. Type up a stem-and-leaf plot chart in the box below for the variable Money, with a space between the stems and the group of leaves in each line. Use the tens value as the stem and the ones value for the leaves.  It may be helpful to sort the data based on the Money variable first.

An example of a stem-and-leaf plot would look like this:

  • 4  5  6  9  3
  • 5  6  3  6
  • 9  2

The stem-and-leaf plot shown above would be for data 4, 5, 6, 9, 3, 15, 16, 13, 16, 29, and 22. (4 points)

Calculating Descriptive Statistics

  1. Calculate descriptive statistics for the variable Height by Gender. Click on Insert and then Pivot Table.  Click in the top box and select all the data (including labels) from Height through Gender.  Also click on “new worksheet” and then OK.  On the right of the new sheet, click on Height and Gender, making sure that Gender is in the Rows box and Height is in the Values   Click on the down arrow next to Height in the Values box and select Value Field Settings.  In the pop up box, click Average then OK.  Type in the averages below.  Then click on the down arrow next to Height in the Values box again and select Value Field Settings.  In the pop up box, click on StdDev then OK.  Type the standard deviations below. (3 points)

Short Answer Writing Assignment

All answers should be complete sentences.

What is the most common color of car for students who participated in this survey? Explain how you arrived at your answer. (5 points)

What is seen in the histogram created for the heights of students in this class (include the shape)? Explain your answer.  (5 points)

What is seen in the stem and leaf plot for the money variable (include the shape)? Explain your answer.  (5 points)

Compare the mean for the heights of males and the mean for the heights of females in these data. Compare the values and explain what can be concluded based on the numbers.   (5 points)

Compare the standard deviation for the heights of males and the standard deviation for the heights of females in the class. Compare the values and explain what can be concluded based on the numbers.  (5 points)

Using the empirical rule, 95% of female heights should be between what two values? Either show work or explain how your answer was calculated.  (5 points)

Using the empirical rule, 68% of male heights should be between what two values? Either show work or explain how your answer was calculated.   (5 points)

Statistics for Decision Making

Lab Week 2

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Statistical Concepts:

  • Using Minitab
  • Graphics
  • Shapes of Distributions
  • Descriptive Statistics
  • Empirical Rule

Data in Minitab

  • Minitab is a powerful, yet user-friendly, data analysis software package. You can launch Minitab by finding the icon and double clicking on it. After a moment you will see two windows, the Session Window in the top half of the screen and the Worksheet or Data Window in the bottom half.
  • Data have already been formatted and entered into a Minitab worksheet. Go to the eCollege Doc sharing site to download this data file. The names of each variable from the survey are in the first row of the Worksheet. This row has a background color of gray to identify it as the variable names. All other rows of the Minitab Worksheet represent a certain students’ answers to the survey questions. Therefore, the rows are called observations and the columns are called variables. Included with this lab, you will find a code sheet that identifies the correspondence between the variable names and the survey questions.
  • Complete the questions after the Code Sheet and paste the Graphs from Minitab in the grey areas for question 1 through 3. Type your answers to questions 4 through 11 where noted in the grey areas. When asked for explanations, please give thorough, multi-sentence or paragraph length explanations. The completed iLab Word Document with your responses to the questions will be the ONE and only document submitted to the dropbox. When saving and submitting the document, you are required to use the following format: Last Name_ First Name_Week2iLab.

Code Sheet

Do NOT answer these questions. The Code Sheet just lists the variables name and the question used by the researchers on the survey instrument that produced the data that are included in the Minitab data file. This is just information. The first question for the lab is after the code sheet….

Statistics for Decision Making

iLab Week 4 

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Statistical Concepts:

  • Probability
  • Binomial Probability Distribution

Calculating Binomial Probabilities

  • Open a new Excel worksheet.
  1. Open spreadsheet
  2. In cell A1 type “success” as the label
  3. Under that in column A, type 0 through 10 (these will be in rows 2 through 12)
  4. In cell B1, type “one fourth”
  5. In cell B2, type “=BINOM.DIST(A2,10,0.25,FALSE)” [NOTE: if you have Excel 2007, then the formula is BINOMDIST without the period]
  6. Then copy and paste this formula in cells B3 through B12
  7. In cell C1, type “one half”
  8. In cell C2, type “=BINOM.DIST(A2,10,0.5,FALSE)”
  9. Copy and paste this formula in cells C3 through C12
  10. In cell D1 type “three fourths”
  11. In cell D2, type “=BINOM.DIST(A2,10,0.75,FALSE)”
  12. Copy and paste this formula in cells D3 through D12

Plotting the Binomial Probabilities

  1. Create plots for the three binomial distributions above. You can create the scatter plots in Excel by selecting the data you want plotted, clicking on INSERT, CHARTS, SCATTER, then selecting the first chart shown which is dots with no connecting lines.  Do this two more times and for graph 2 set Y equal to ‘one half’ and X to ‘success’, and for graph 3 set Y equal to ‘three fourths’ and X to ‘success’.  Paste those three scatter plots in the grey area below.  (9 points)

Calculating Descriptive Statistics

  • You will use the same class survey results that were entered into the worksheet for the Week 2 iLab Assignment for question 2.
  1. Calculate descriptive statistics for the variable (Coin) where each of the thirty-five students flipped a coin 10 times. Round your answers to three decimal places and type the mean and the standard deviation in the grey area below. (5 points)

Short Answer Writing Assignment – Both the calculated binomial probabilities and the descriptive statistics from the class database will be used to answer the following questions.  Round all numeric answers to three decimal places.

  1. List the probability value for each possibility in the binomial experiment calculated at the beginning of this lab, which was calculated with the probability of a success being ½. (Complete sentence not necessary; round your answers to three decimal places) (8 points)
P(x=0)P(x=6)
P(x=1)P(x=7)
P(x=2)P(x=8)
P(x=3)P(x=9)
P(x=4)P(x=10)
P(x=5)
  1. Give the probability for the following based on the calculations in question 3 above, with the probability of a success being ½. (Complete sentence not necessary; round your answers to three decimal places) (8 points)

Statistics for Decision Making

P(x≥1)P(x<0)
P(x>1)P(x≤4)
P(4<x ≤7)P(x<4 or x≥7)
  1. Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ½ and n = 10. Either show work or explain how your answer was calculated. Use these formulas to do the hand calculations: Mean = np, Standard Deviation = (4 points)
  2. Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ¼ and n = 10. Write a comparison of these statistics to those from question 5 in a short paragraph of several complete sentences. Use these formulas to do the hand calculations: Mean = np, Standard Deviation = (4 points)
  3. Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ¾ and n = 10. Write a comparison of these statistics to those from question 6 in a short paragraph of several complete sentences. Use these formulas to do the hand calculations: Mean = np, Standard Deviation = (4 points)
  4. Using all four of the properties of a Binomial experiment (see page 201 in the textbook) explain in a short paragraph of several complete sentences why the Coin variable from the class survey represents a binomial distribution from a binomial experiment. (4 points)
  5. Compare the mean and standard deviation for the Coin variable (question 2) with those of the mean and standard deviation for the binomial distribution that was calculated by hand in question 5. Explain how they are related in a short paragraph of several complete sentences. (4 points)
Mean from question #

Standard deviation from question #…

Statistics for Decision Making

Lab Week 4

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Statistical Concepts:

  • Probability
  • Binomial Probability Distribution

Calculating Binomial Probabilities

  • Open a new MINITAB worksheet.
  • We are interested in a binomial experiment with 10 trials. First, we will make the probability of a success ¼. Use MINITAB to calculate the probabilities for this distribution. In column C1 enter the word ‘success’ as the variable name (in the shaded cell above row 1. Now in that same column, enter the numbers zero through ten to represent all possibilities for the number of successes. These numbers will end up in rows 1 through 11 in that first column. In column C2 enter the words ‘one fourth’ as the variable name. Pull up Calc > Probability Distributions > Binomial and select the radio button that corresponds to Probability. Enter 10 for the Number of trials: and enter 0.25 for the Event probability:. For the Input column: select ‘success’ and for the Optional storage: select ‘one fourth’. Click the button OK and the probabilities will be displayed in the Worksheet.
  • Now we will change the probability of a success to ½. In column C3 enter the words ‘one half’ as the variable name. Use similar steps to that given above in order to calculate the probabilities for this column. The only difference is in Event probability: use 0.5.
  • Finally, we will change the probability of a success to ¾. In column C4 enter the words ‘three fourths’ as the variable name. Again, use similar steps to that given above in order to calculate the probabilities for this column. The only difference is in Event probability: use 0.75.

Plotting the Binomial Probabilities

  1. Create plots for the three binomial distributions above. Select Graph > Scatter Plot and Simple then for graph 1 set Y equal to ‘one fourth’ and X to ‘success’ by clicking on the variable name and using the “select” button below the list of variables.  Do this two more times and for graph 2 set Y equal to ‘one half’ and X to ‘success’, and for graph 3 set Y equal to ‘three fourths’ and X to ‘success’.  Paste those three scatter plots below.

Calculating Descriptive Statistics

  • Open the class survey results that were entered into the MINITAB worksheet.
  1. Calculate descriptive statistics for the variable where students flipped a coin 10 times. Pull up Stat > Basic Statistics > Display Descriptive Statistics and set Variables: to the coin. The output will show up in your Session Window. Type the mean and the standard deviation here.

Short Answer Writing Assignment – Both the calculated binomial probabilities and the descriptive statistics from the class database will be used to answer the following questions.

  1. List the probability value for each possibility in the binomial experiment that was calculated in MINITAB with the probability of a success being ½. (Complete sentence not necessary)
  2. Give the probability for the following based on the MINITAB calculations with the probability of a success being ½. (Complete sentence not necessary)
  3. Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ½. Either show work or explain how your answer was calculated. Mean = np, Standard Deviation =
  4. Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ¼ and compare to the results from question 5. Mean = np, Standard Deviation =
  5. Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ¾ and compare to the results from question 6. Mean = np, Standard Deviation =
  6. Explain why the coin variable from the class survey represents a binomial distribution.
  7. Give the mean and standard deviation for the coin variable and compare these to the mean and standard deviation for the binomial distribution that was calculated in question 5. Explain how they are related. Mean = np, Standard Deviation =

Statistics for Decision Making

iLab Week 6

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Statistical Concepts:

  • Data Simulation
  • Confidence Intervals
  • Normal Probabilities

Short Answer Writing Assignment

All answers should be complete sentences.

We need to find the confidence interval for the SLEEP variable.  To do this, we need to find the mean and then find the maximum error.  Then we can use a calculator to find the interval, (x – E, x + E).

First, find the mean.  Under that column, in cell E37, type =AVERAGE(E2:E36).  Under that in cell E38, type =STDEV(E2:E36).   Now we can find the maximum error of the confidence interval.  To find the maximum error, we use the “confidence” formula.  In cell E39, type =CONFIDENCE.NORM(0.05,E38,35).  The 0.05 is based on the confidence level of 95%, the E38 is the standard deviation, and 35 is the number in our sample.  You then need to calculate the confidence interval by using a calculator to subtract the maximum error from the mean (x-E) and add it to the mean (x+E).

  1. Give and interpret the 95% confidence interval for the hours of sleep a student gets. (5 points)

Then, you can go down to cell E40 and type =CONFIDENCE.NORM(0.01,E38,35) to find the maximum error for a 99% confidence interval.  Again, you would need to use a calculator to subtract this and add this to the mean to find the actual confidence interval.

  1. Give and interpret the 99% confidence interval for the hours of sleep a student gets. (5 points)
  1. Compare the 95% and 99% confidence intervals for the hours of sleep a student gets. Explain the difference between these intervals and why this difference occurs. (5 points)

In the week 2 lab, you found the mean and the standard deviation for the HEIGHT variable for both males and females.  Use those values for follow these directions to calculate the numbers again.

(From week 2 lab: Calculate descriptive statistics for the variable Height by Gender.  Click on Insert and then Pivot Table.  Click in the top box and select all the data (including labels) from Height through Gender.  Also click on “new worksheet” and then OK.  On the right of the new sheet, click on Height and Gender, making sure that Gender is in the Rows box and Height is in the Values box.   Click on the down arrow next to Height in the Values box and select Value Field Settings.  In the pop up box, click Average then OK.  Write these down.  Then click on the down arrow next to Height in the Values box again and select Value Field Settings.  In the pop up box, click on StdDev then OK.  Write these values down.)

You will also need the number of males and the number of females in the dataset.  You can either use the same pivot table created above by selecting Count in the Value Field Settings, or you can actually count in the dataset.

Then in Excel (somewhere on the data file or in a blank worksheet), calculate the maximum error for the females and the maximum error for the males.  To find the maximum error for the females, type =CONFIDENCE.T(0.05,stdev,#), using the females’ height standard deviation for “stdev” in the formula and the number of females in your sample for the “#”.  Then you can use a calculator to add and subtract this maximum error from the average female height for the 95% confidence interval.  Do this again with 0.01 as the alpha in the beginning of the formula to find the 99% confidence interval.

Find these same two intervals for the male data by using the same formula, but using the males’ standard deviation for “stdev” and the number of males in your sample for the “#”.

  1. Give and interpret the 95% confidence intervals for males and females on the HEIGHT variable.  Which is wider and why?  (7 points)
  1. Give and interpret the 99% confidence intervals for males and females on the HEIGHT variable.  Which is wider and why?  (7 points)
  1. Find the mean and standard deviation of the DRIVE variable by using =AVERAGE(A2:A36) and =STDEV(A2:A36). Assuming that this variable is normally distributed, what percentage of data would you predict would be less than 40 miles?  This would be based on the calculated probability.  Use the formula =NORM.DIST(40, mean, stdev,TRUE).  Now determine the percentage of data points in the dataset that fall within this range.  To find the actual percentage in the dataset, sort the DRIVE variable and count how many of the data points are less than 40 out of the total 35 data points.  That is the actual percentage.  How does this compare with your prediction?   (10 points)
Mean ______________             Standard deviation ____________________

Predicted percentage ______________________________

Actual percentage _____________________________

Comparison ___________________________________________________

______________________________________________________________

  1. What percentage of data would you predict would be between 40 and 70 and what percentage would you predict would be more than 70 miles? Subtract the probabilities found through =NORM.DIST(70, mean, stdev, TRUE) and =NORM.DIST(40, mean, stdev, TRUE) for the “between” probability.  To get the probability of over 70, use the same =NORM.DIST(70, mean, stdev, TRUE) and then subtract the result from 1 to get “more than”.  Now determine the percentage of data points in the dataset that fall within this range, using same strategy as above for counting data points in the data set.  How do each of these compare with your prediction and why is there a difference?   (11 points
Predicted percentage between 40 and 70 ______________________________

Actual percentage _____________________________________________

Predicted percentage more than 70 miles ________________________________

Actual percentage ___________________________________________

Comparison ____________________________________________________

_______________________________________________________________

Why?  __________________________________________________________

________________________________________________________________

Statistics for Decision Making

Lab Week 6 

https://www.hiqualitytutorials.com/product/math-221-ilab-week-6/

This is a new lab, but the most recent lab is available here:

Statistical Concepts:

  • Data Simulation
  • Confidence Intervals
  • Normal Probabilities

Short Answer Writing Assignment

All answers should be complete sentences.

We need to find the confidence interval for the SLEEP variable.  To do this, we need to find the mean and then find the maximum error.  Then we can use a calculator to find the interval, (x – E, x + E).

First, find the mean.  Under that column, in cell E37, type =AVERAGE (E2:E36).  Under that in cell E38, type =STDEV (E2:E36).   Now we can find the maximum error of the confidence interval.  To find the maximum error, we use the “confidence” formula.  In cell E39, type =CONFIDENCE.NORM (0.05, E38, 35).  The 0.05 is based on the confidence level of 95%, the E38 is the standard deviation, and 35 is the number in our sample.  You then need to calculate the confidence interval by using a calculator to subtract the maximum error from the mean (x-E) and add it to the mean (x+E).

  1. Give and interpret the 95% confidence interval for the hours of sleep a student gets. (6 points)
  2. Give and interpret the 99% confidence interval for the hours of sleep a student gets. (6 points)
  3. Compare the 95% and 99% confidence intervals for the hours of sleep a student gets. Explain the difference between these intervals and why this difference occurs. (6 points)
  4. Give and interpret the 95% confidence intervals for males and females on the HEIGHT variable. Which is wider and why?  (9 points)
  5. Give and interpret the 99% confidence intervals for males and females on the HEIGHT variable. Which is wider and why?  (9 points)
  6. Find the mean and standard deviation of the DRIVE variable by using =AVERAGE(A2:A36) and =STDEV(A2:A36). Assuming that this variable is normally distributed, what percentage of data would you predict would be less than 40 miles?  This would be based on the calculated probability.  Use the formula =NORM.DIST(40, mean, stdev,TRUE).  Now determine the percentage of data points in the dataset that fall within this range.  To find the actual percentage in the dataset, sort the DRIVE variable and count how many of the data points are less than 40 out of the total 35 data points.  That is the actual percentage.  How does this compare with your prediction?   (12 points)
  7. What percentage of data would you predict would be between 40 and 70 and what percentage would you predict would be more than 70 miles? Subtract the probabilities found through =NORM.DIST(70, mean, stdev, TRUE) and =NORM.DIST(40, mean, stdev, TRUE) for the “between” probability.  To get the probability of over 70, use the same =NORM.DIST(70, mean, stdev, TRUE) and then subtract the result from 1 to get “more than”.  Now determine the percentage of data points in the dataset that fall within this range, using same strategy as above for counting data points in the data set.  How do each of these compare with your prediction and why is there a difference?   (12 points)

Statistics for Decision Making

 iLab Week 6 

https://www.hiqualitytutorials.com/product/math221-lab-week-6/

Statistical Concepts:

  • Data Simulation
  • Discrete Probability Distribution
  • Confidence Intervals

Calculations for a set of variables

  • Open the class survey results that were entered into the MINITAB worksheet.
  • We want to calculate the mean for the 10 rolls of the die for each student in the class. Label the column next to die10 in the Worksheet with the word mean. Pull up Calc > Row Statistics and select the radio-button corresponding to Mean. For Input variables: enter all 10 rows of the die data. Go to the Store result in: and select the mean Click OK and the mean for each observation will show up in the Worksheet.
  • We also want to calculate the median for the 10 rolls of the die. Label the next column in the Worksheet with the word median. Repeat the above steps but select the radio-button that corresponds to Median and in the Store results in: text area, place the median

Calculating Descriptive Statistics

  • Calculate descriptive statistics for the mean and median columns that where created above. Pull up Stat > Basic Statistics > Display Descriptive Statistics and set Variables: to mean and median. The output will show up in your Session Window. Print this information.

Calculating Confidence Intervals for one Variable

  • Open the class survey results that were entered into the MINITAB worksheet.
  • We are interested in calculating a 95% confidence interval for the hours of sleep a student gets. Pull up Stat > Basic Statistics > 1-Sample t and set Samples in columns: to Sleep. Click the OK button and the results will appear in your Session Window.
  • We are also interested in the same analysis with a 99% confidence interval. Use the same steps except select the Options button and change the Confidence level: to 99. Short Answer Writing Assignment

All answers should be complete sentences.

Statistics for Decision Making

Quiz Week 3 Recent

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  1. Determine whether the given value is a statistic or a parameter.

In a study of all 2300 students at a college comma it is found that 55 % own a computer.In a study of all 2300 students at a college, it is found that 55% own a computer.

Choose the correct statement below.

Parameter because the value is a numerical measurement describing a characteristic of a population.

Statistic because the value is a numerical measurement describing a characteristic of a population.

Statistic because the value is a numerical measurement describing a characteristic of a sample

Parameter because the value is a numerical measurement describing a characteristic of a sample

  1. The mean value of land and buildings per acre from a sample of farms is $15001500​, with a standard deviation of $300300. The data set has a​ bell-shaped distribution. Using the empirical​ rule, determine which of the following​ farms, whose land and building values per acre are​ given, are unusual​ (more than two standard deviations from the​ mean). Are any of the data values very unusual​ (more than three standard deviations from the​ mean)?

​$2083

​$2309

​$1779

​$359

​$2084

​$2009

Which of the farms are unusual​ (more than two standard deviations from the​ mean)? Select all that apply.

$2084

$2083

$359

$2309

$1779

$2009

Which of the farms are very (more than three standard deviations from the mean)?  Select all that apply.

$2009

$359

$2309

$2084

$1779

$2083

None of the data values are very unusual

  1. Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.​(The pair of variables have a significant​ ) Then use the regression equation to predict the value of y for each of the given​ x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.

Find the regression equation

Choose the correct graph below

Predict the value of y for x=2.  Choose the correct answer below.

38.0

41.7

52.7

Not meaningful

Predict the value of y for x=3.5.  Choose the correct answer below.

38.0

137.3

52.7

Not meaningful

Predict the value of y for x=15.  Choose the correct answer below.

41.7

137.3

52.7

Not meaningful

Predict the value of y for x=1.5.  Choose the correct answer below.

38.0

41.7

137.3

Not meaningful

  1. Identify the sampling techniques ​used, and discuss potential sources of bias​ (if any). Explain.

In​1965, researchers used random digit dialing to call 1200 people and ask what obstacles kept them from voting.

What type of sampling was used?

  1. Convenience sampling was used, since the 1200 phone numbers that were easiest to reach were selected.
  2. Cluster sampling was used, since phone numbers were divided into groups, several groups were selected, and each number in those groups was called.
  3. Systematic sampling was used since phone numbers were selected from a list using a fixed interval between phone numbers.
  4. Simple random sampling was used, since each number had an equal chance of being dialed, so all samples of 1200 phone numbers had an equal chance of being selected.

What potential sources of bias were present, if any?  Select all that apply.

  1. Individuals may have refused to participate in the sample. This may have made the sample less representative of the population.
  2. The sample only consisted of members of the population that were easy to get. These members may have not been representative of the population.
  3. Individuals may have not been available when the researchers were calling. Those individuals that were available may have not been representative of the population.
  4. Telephone sampling only includes people who had telephones. People who owned telephones may have been older or wealthier on average, and may not have been representative of the entire population.
  5. There were no potential sources of bias.
  1. Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.​(Each pair of variables has a significant​ ) Then use the regression equation to predict the value of y for each of the given​ x-values, if meaningful. The caloric content and the sodium content​ (in milligrams) for 6 beef hot dogs are shown in the table below.

Find the regression equation.

Choose the correct graph below

Predict the value of y for x =150.  Choose the correct answer below.

425.833

398.333

178.333

Not meaningful

Predict the value of y for x =90.  Choose the correct answer below.

178.333

398.333

260.833

Not meaningful

Predict the value of y for x =140.  Choose the correct answer below.

425.833

398.333

260.833

Predict the value of y for x =60.  Choose the correct answer below.

178.333

260.833

425.833

Not meaningful

7.

  1. Suppose the scatter plot shows the results of a survey of 41 randomly selected males ages 24 to 35. Using age as the explanatory variable, choose the appropriate description for the graph.  Explain your reasoning.
  2. 9. Determine whether the underlined value is a parameter or a statistic.

One of greatest baseball hitters of all time has a career batting average of…

Is the value a parameter or a statistic?

  1. 10. Match the plot with a possible description of the sample.

Choose the correct answer below.

  1. Ages (in years) of a sample of residents of a retirement home
  2. Time (in hours) spent watching TV in a day for a sample of teenagers
  3. Top speeds (in miles per hour) of a sample of sports cars
  4. Waiting time (in minutes) for a sample of doctors’ offices

11 Determine whether the following statement is true or false. If it is​ false, rewrite it as a true statement.

For data at the interval​ level, you cannot calculate meaningful differences between data entries.

Choose the correct answer below.

  1. The statement is true
  2. The statement is false. A true statement is “For data at the interval level, you can’t order them, but you can calculate meaningful differences between data entries.”
  3. The statement is false. A true statement is “For data at the interval level, you cannot calculate meaningful differences between data entries.”
  4. The statement is false. A true statement is “For data at the interval level, you can calculate meaningful differences between date entries.”
  1. The plot does not show all the data. It only shows the prices that fall between $200 and $260 inclusive.
  2. The plot gives an overview of all the data. It clearly shows that the prices fall between $209 and $252 inclusive.
  3. The plot does not show all the data. It only shows the prices that fall between $209 and $252 inclusive.
  4. The plot gives an overview of all the data. It clearly shows that the prices fall between $200 and $260 inclusive.
    1. 13. Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression​ line? About the unexplained​ variation?
  5. r=0.852Calculate the coefficient of determinationWhat does this tell you about the explained variation of the data about the regression line?% of the variation can be explained by the regression line.

About the unexplained variation?

% of the variation is unexplained and is due to other factors or to sampling error.

14.

Quantitative

Qualitative

What is the data set’s level of measurement?

Interval

Ratio

Nominal

Ordinal

  1. Match this description with a description below.

Choose the correct answer below.

  1. 16. The ages of 10 brides at their first marriage are given below. Complete parts​(a) and​(b)

Find the range of the data set

Range=

Change 43.3 to 53.8 and find the range of the new data set.

Range=

Statistics for Decision Making

Quiz Week 3 

https://www.hiqualitytutorials.com/product/math221-quiz-week-3/

    1. Use the Venn diagram to identify the population and the sample.

Choose the correct description of the population.

  1.  The number of home owners in the state
    B.  The income of home owners in the state who own a car
    C.  The income of home owners in the state
    D.  The number of home owners in the state who own a car

Choose the correct description of the sample

  1.  The income of home owners in the state who own a car
    B.  The income of home owners in the state
    C.  The number of home owners in the state who own a car
    D.  The number of home owners in the state
    1. Determine whether the variable is qualitative or quantitative.

Favorite sport

Is the variable qualitative or quantitative?

  1.  Qualitative
    B.  Quantitative
    1. Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 30 students. The scores are shown below.

43  50  10  91  76  35  64  36  42  72  53  62  35  74  50
72  36  28  38  61  48  63  35  41  22  36  50  46  85  13

To find the 10% trimmed mean of a data set, order the data, delete the lowest 10% of the entries and highest 10% of the entries, and find the mean of the remaining entries.  Complete parts (a) through (c).

(a) Find the 10% trimmed mean for the data.
The 10% trimmed mean is.  (Round to the nearest tenth as needed.)
(b) Compare the four measures of central tendency, including the midrange.
Mean =  (Round to the nearest tenth as needed.)
Median =
Mode =  (Use a comma to separate answers as needed.)
Midrange =  (Round to the nearest tenth as needed.)

(c) What is the benefit of using a trimmed mean versus using a mean found using all data entries?

  1.  It simply decreases the number of computations in finding the mean.
    B.  It permits the comparison of the measures of central tendency.
    C.  It permits finding the mean of a data set more exactly.
    D.  It eliminates potential outliers that could affect the mean of the entries.
    1. Construct a frequency distribution for the given data set using 6 classes. In the table, include the midpoints, relative frequencies, and cumulative frequencies. Which class has the greatest frequency and which has the least frequency?

Amount (in dollars) spent on books for a semester

457  146  287  535  442  543  46  405  496  385  517  56  33  132  64
99  378  145  30  419  336  228  376  227  262  340  172  116  285

Complete the table, starting with the lowest class limit.  Use the minimum data entry as the lower limit of the first class. (Type integers or decimals rounded to the nearest thousandth as needed.)

Which class has the greatest frequency?
The class with the greatest frequency is from  to.
Which class has the least frequency?
The class with the least frequency is from to.

    1. Identify the data set’s level of measurement.

The nationalities listed in a recent survey (for example, American, German, or Brazilian)

  1.  Nominal
    B.  Ordinal
    C.  Interval
    D.  Ratio
    1. Explain the relationship between variance and standard deviation. Can either of these measures be negative?

Choose the correct answer below.

  1.  The standard deviation is the negative square root of the variance. The standard deviation can be negative but the variance can never be negative.
    B.  The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative.  Squared deviations can never be negative.
    C.  The variance is the negative square root of the standard deviation. The variance can be negative but the standard deviation can never be negative.
    D.  The variance is the positive square root of the standard deviation. The standard deviation and variance can never be negative.  Squared deviations can never be negative.
    1. For the following data (a) display the data in a scatter plot, (b) calculate the correlation coefficient r, and (c) make a conclusion about the type of correlation.

The number of hours 6 students watched television during the weekend and the scores of each student who took a test the following Monday.

Hours spent watching TV, x   0          1          2          3          3          5

Test score, y                            98        90        84        74        93        65

(a) Choose the correct scatter plot below.

(b) The correlation coefficient r is (Round to three decimal places as needed)
(c) Which of the following best describes the type of correlation that exists between number of hours spent watching television and test scores?

  1.  Strong negative linear correlation
    B.  No linear correlation
    C.  Weak negative linear correlation
    D.  Strong positive linear correlation
    E.  Weak positive linear correlation
    1. Suppose a survey of 526 women in the United States found that more than 70% are the primary investor in their household. Which part of the survey represents the descriptive branch of statistics?

Choose the best statement of the descriptive statistic in the problem.

  1.  There is an association between the 526 women and being the primary investor in their household.
    B.  526 women were surveyed.
    C.  70% of women in the sample are the primary investor in their household.
    D.  There is an association between U.S. women and being the primary investor in their household.
    Choose the best inference from the given information.
  2.  There is an association between the 526 women and being the primary investor in their household.
    B.  There is an association between U.S. women and being the primary investor in their household.
    C.  70% of women in the sample are the primary investor in their household
    D.  526 women were surveyed.
    1. Identify the sampling technique used.

A community college student interviews everyone in a particular statistics class to determine the percentage of students that own a car.

  1.  Random
    B.  Cluster
    C.  Convenience
    D.  Stratified
    E.  Systematic
    1. Use the frequency polygon to identify the class with the greatest, and the class with the least frequency.

What are the boundaries of the class with the greatest frequency?

  1.  25.5-30.5
    B.  25-31
    C.  26.5-29.5
    D.  28-31

What are the boundaries of the class with the least frequency?

  1.  10-13
    B.  5-11.5
    C.  7-13
    D.  5-12.5
    1. Determine whether the given value is a statistic or a parameter

In a study of all 2377 students at a college, it is found that 35% own a computer

Choose the correct statement below.

  1.  Parameter because the value is a numerical measurement describing a characteristic of a population.
    B.  Statistic because the value is a numerical measurement describing a characteristic of a population.
    C.  Statistic because the value is a numerical measurement describing a characteristic of a sample.
    D.  Parameter because the value is a numerical measurement describing a characteristic of a sample.
    1. Compare the three data sets

(a) Which data set has the greatest sample standard deviation?

  1.  Data set (iii), because it has more entries that are farther away from the mean
    B.  Data set (ii), because it has two entries that are far away from the mean.
    C.  Data set (i), because it has more entries that are close to the mean.

Which data set has the least sample standard deviation?

  1.  Data set (i), because it has more entries that are close to the mean.
    B.  Data set (ii), because it has less entries that are farther away from the mean.
    C.  Data set (iii), because it has more entries that are farther away from the mean.

(b) How are the data sets the same? How do they differ?

  1.  The three data sets have the same standard deviations but have different means.
    B.  The three data sets have the same mean, median and mode but have different standard deviation.
    C.  The three data sets have the same mean and mode but have different medians and standard deviations.
    D.  The three data sets have the same mode but have different standard deviations and means
    1. Decide which method of data collection you would use to collect data for the study.

A study of the effect on the human digestive system of a popular soda made with a caffeine substitute.

Choose the correct answer below.

  1.  Observational Study
    B.  Simulation
    C.  Survey
    D.  Experiment
    1. Use the given frequency distribution to find the:
    • (a) Class width
    • (b) Class midpoint of the first class
    • (c) Class boundaries of the first class
  1.  (a) 4 (b) 137.5 (c) 134.5-139.5
    B.  (a) 5 (b) 137 (c) 135-139
    C.  (a) 5 (b) 137 (c) 134.5-139.5
    D.  (a) 4 (b) 137.5 (c) 135-139
    1. Consider the following sample data values.

5          14        15        21        16        13        9          19

(a) Calculate the range
(b) Calculate the variance
(c) Calculate the standard deviation

  1.  The range is. (Type an integer or a decimal)
    b.  The sample variance is. (Type an integer or decimal rounded to two decimal places as needed)
    c.  The sample standard deviation is. (Type an integer or decimal rounded to two decimal places as needed)
    1. Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.  (the pair of variables have a significant correlation.)  Then use the regression equation to predict the value of y for each of the given x-values, if meaningful.  The number of hours 6 students spent for a test and their scores on that test are shown below.

Find the regression equation.

^

Y = x + () (Round to three decimal places as needed)

Choose the correct graph below.

(a)  Predict the value of y for x = 4. Choose the correct answer below.

    1. 1
    2. 8
    3. 8
    4. Not meaningful
    • (b) Predict the value of y for x = 4.5. Choose the correct answer below.
    1. 1
    2. 8
    3. 0
    4. Not meaningful

(c)  Predict the value of y for x = 12.  Choose the correct answer below.

    1. 8
    2. 1
    3. 0
    4. Not meaningful

(d) Predict the value of y for x = 2.5. Choose the correct answer below.

  1.  57.8
    B.  47.8
    C.  111.0
    D.  Not meaningful

1.Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 20 students. The scores are given below.
27 15 39 43 23 14 49 33 57 35
36 14 13 38 22 24 22 48 14 23

    1. Suppose that a study based on a sample from a targeted population shows that people at a pizza restaurant are hungrier than people at a coffee shop.
      A) make an inference based on the results of this study.
      B) what might this inference incorrectly imply?

3.Decide which method of data collecting you would use to collect data for the study below:
A study of how fast a virus would spread in a school of fish.

    1. Identify the sampling technique used:
      The name of 50 contestants are written on 50 cards. The cards are placed in a bag, and three names are picked from the bag.

5.In a poll of 1002 women in a country were asked whether they favor or oppose of the use of federal tax dollars to fund medical research using stem cells obtained from embryos. Among the women, 48% said they were in favor.

    1. Identify the data set’s level of measurement.
      The years the summer Olympics were held in a particular country

7.Use the frequency histogram to answer each question.
A) determine the # of classes
B) estimate the frequency of the class with the least frequency.
C) estimate the frequency of the class with the greatest frequency.
D) determine the class width.

8.The data represents the time, in minutes, spent reading a political blog in a day. Construct a frequency distribution using 5 classes. In the table, include midpoints, relative frequencies, and cumulative frequencies. Which class had the greatest and least frequency?

    1. Given a data set, how do you know whether to calculate σ or s?

10.Compare the three data sets on the right.

11.Use the given minimum and maximum data entries and the number of classes to find class width, lower class limits, and upper class limits.
min = 9, max = 83, classes = 6

12.Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The table below shows the heights (in feet) and the number of stories of six notable buildings in a city.

13.For the following data (a) display the data in a scatter plat, (b) calculate the correlation coefficient r, and (c) make a conclusion about the type of correlation.
The ages (in years) of 6 children and the number of words in their vocabulary.

Age, X123456
Vocabulary Size3509501200170022502600

14.Determine whether the underlined numerical value is a parameter or a statistic. In a poll of a sample of 12,000 adults, in a certain city, 12% said they left for work before 6am.

15.Both data sets have a mean of 225. One has a SD of 16 and the other has an SD of 24.

16.Use the Venn diagram to identify the population and the sample.

17.Determine whether the variable is qualitative or quantitative. Breed of cat.

18.Use the relative frequency histogram below to complete each part.
A) identify the class with the greatest and the class with the least frequency.
B) approximate the greatest and least relative frequencies.
C) approximate the relative frequency of the second class.

19.Use the given frequency distribution to find the:
A) class width
B) class midpoint of the first class
C) class boundaries of the first class.

Height (in inches)
ClassFrequency
50-525
53-558
56-5812
59-6113
62-6411

Statistics for Decision Making

20.For the following data (a) display the data in a scatter plot, (b) calculate the correlation coefficient r, and (c) make a conclusion about that type of correlation.
The number of hours 6 students watched television during the weekend and the scores of each student who took a test the following monday.

Hours spent Watching TV012335
Test Score988986708166

21.Explain the relationship below between variance and standard deviation. Can either of these measures be negative?

22.Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 30 students. The scores are shown below.
44        50        10        91        77        35        64        36        43        72        54        62        35        75        50

72        36        29        39        61        49        63        35        41        21        36        50        47        86        13

To find the 10% trimmed mean of a data set, order the data, delete the lowest and highest 10% of the entries

23.Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (the pair of variables have a significant correlation.) then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.

    1. Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning.
      the average grade on the midterm exam in a certain math class of 50 students was an 88.

25.Suppose that a study based on a sample from a targeted population shows that people who own a fax machine have more money than people who do not.
A) Make an inference based on the results of this study.
B) What might this inference incorrectly imply?

    1. Identify the data set’s level of measurement.
      The average daily temperatures (in degrees Fahrenheit) on five randomly selected days.
      23, 33, 28, 34, 35

27.Identify the sampling technique used.
The name of 100 contestants are written on 100 cards. The cards are placed in a bag, and three names are picked from the bag.

28.Which method of data collection should be used to collect data for the following study.
The average weight of 175 students in a high school.

Statistics for Decision Making

Quiz Week 5 Recent

https://www.hiqualitytutorials.com/product/quiz-week-5-recent/

  1. The table below shows the results of a survey in which 141 men and 145 women workers ages 25-64 were asked if they have at least one month’s income set aside for emergencies. complete parts (a) – (d)

A =
B =
C =
D =

2.

Mean = 2.44
Variance = 1.8864
Standard deviation = 1.3735
Expected value =

  1. 3. A doctor gives a patient a 60​% chance of surviving bypass surgery after a heart attack. If the patient survives the​ surgery, then the patient has a 20​% chance that the heart damage will heal. Find the probability that the patient survives the surgery and the heart damage heals.
  2. Perform the indicated calculation.

5 A standard deck of cards contains 52 cards. One card is selected from the deck.

  1. 6. Determine the required value of the missing probability to make the distribution a discrete probability distribution.

P(4)=

  1. 7. Determine whether the events E and F are independent or dependent. Justify your answer.
  1. E & F are dependent because being prone to road rage can affect the probability of a person having an at-fault accident.
    B. E cannot affect F and vice versa because the people were randomly selected, so all events are independent.
    C.  The war in major oil exporting country could affect the price of gasoline, so E and F are dependent.
  2. 8. During a​ 52-week period, a company paid overtime wages for 17 weeks and hired temporary help for

77 weeks. During 55 weeks, the company paid overtime and hired temporary help. Complete parts​ (a) and​ (b) below.

A=

Overtime=

  1. 9. About 40​% of babies born with a certain ailment recover fully. A hospital is caring for six babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it​ is, identify a​ success, specify the values of​ n, p, and​ q, and list the possible values of the random variable x.

Is the experiment a bionomial experiment?

What is a success in this experiment?

Specify the value of n.  Select the correct choice below and fill in any answer boxes in your choice.

Specify the value of p.  Select the correct choice below and fill in any answer boxes in your choice.

Specify the value of q.  Select the correct choice below and fill in any answer boxes in your choice.

The probability that the highest level of education for an employee chosen at random is B is…

  1. A probability experiment consists of rolling a fair 18​-sided die. Find the probability of the event below. rolling a number divisible by 6.

The probability is…

  1. 12. Suppose Jim is going to burn a compact disk​ (CD) that will contain 88 In how many ways can Jim arrange the 88 songs on the​ CD?
  2. 13. Use the frequency​ distribution, which shows the number of American voters​ (in millions) according to​ age, to find the probability that a voter chosen at random is in the 18 to 20 years old age range.

The probability that a voter chosen at random is in the 18 to 20 years old age range is…

  1. 14. Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities.

Assume the probability that you will make a sale on any given telephone call is 0.250.25.

Find the probability that you​ (a) make your first sale on the fifth​ call, (b) make your sale on the​ first, second, or third​ call, and​ (c) do not make a sale on the first three calls.

  1. P(make your first sale on the fifth call)=
  2. P(make your sale on the first, second, or third call)=
  3. P(do not make a sale on the first three calls)=
  4. =
  1.    15. Determine whether the random variable is discrete or continuous.
  1. The number of free dash throw attempts before the first shot is made number of free throw attempts before the first shot is made.The number of people with blood type Upper A in a random sample of 47 peoplenumber of people with blood type A in a random sample of 47 people.The amount of rain in City Upper B during April amount of rain in City B during April.The number of bald eagles in the country number of bald eagles in the country.

The weight of a Upper T dash bone steak weight of a T-bone steak.

Is the number of free-throw attempts before the first shot is made discrete or continuous?

Is the number of people with blood type A in a random sample of 47 people discrete or continuous?

Is the amount of rain in City B during April discrete or continuous?

Is the number of bald eagles in the country discrete or continuous?

Is the weight of a T-bone steak discrete or continuous?

  1. 16. Find the​ mean, variance, and standard deviation of the binomial distribution with the given values of n and p.

n equals 90n=90​,

p equals 0.3

Mean =

Variance =
Standard deviation=

  1. 17. 38 ​% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of college students who say they use credit cards because of the rewards program is​ (a) exactly​ two, (b) more than​ two, and​ (c) between two and five inclusive. If​ convenient, use technology to find the probabilities.P(2)=P(x>2)=P(2>x<5)=
  2. 18. Use technology to​ (a) construct and graph a probability distribution and​ (b) describe its shape.

The number of computers per household in a small town

  1. Construct the probability distribution per household in a small town
  2. Describe the distribution’s shape. Choose the correct answer below.

Skewed left

Symmetric

Skewed right

Statistics for Decision Making

Quiz Week 5

https://www.hiqualitytutorials.com/product/math221-quiz-week-5/

    1. Sixty percent of households say they would feel secure if they had $50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had $50,000 in savings.  Find the probability that the number that say they would feel secure is (a) exactly five, (b) more than five, and (c) at most five.

(a) Find the probability that the number that say they would feel secure is exactly five

P(5) = (Round to three decimal places as needed)

(b) Find the probability that the number that say they would feel secure is more than five.

P(x>5) = (Round to three decimal places as needed)

(c) Find the probability that the number that say they would feel secure is at most five.

P(x≤5) = (Round to three decimal places as needed)

    1. Suppose 80% of kids who visit a doctor have a fever, and 25% of kids with a fever have sore throats. What’s the probability that a kid who goes to the doctor has a fever and a sore throat?

The probability is. (Round to three decimal places as needed)

    1. Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 90, p = 0.8

The mean, µ is (Round to the nearest tenth as needed)

The variance, σ2, is (Round to the nearest tenth as needed)

The standard deviation, σ is (Round to the nearest tenth as needed)

    1. Use the bar graph below, which shows the highest level of education received by employees of a company, to find the probability that the highest level of education for an employee chosen at random is E.

The probability that the highest level of education for an employee chosen at random is E is.  (Round to the nearest thousandth as needed)

    1. A company that makes cartons finds that the probability of producing a carton with a puncture is 0.05, the probability that a carton has a smashed corner is 0.09, and the probability that a carton has a puncture and has a smashed corner is 0.005. Answer parts (a) and (b) below.
    • Are the events “selecting a carton with a puncture” and “selecting a carton with a smashed corner” mutually exclusive?
    • A. No, a carton can have a puncture and a smashed corner.
    1. Yes, a carton can have a puncture and a smashed corner
    2. Yes, a carton cannot have a puncture and a smashed corner
    3. Mo, a carton cannot have a puncture and a smashed corner
    • If a quality inspector randomly selects a carton, find the probability that the carton has a puncture or has a smashed corner.

The probability that a carton has a puncture or a smashed corner is 0.135.  (Type an integer or a decimal.  Do not round)

    1. Given that x has a Poisson distribution with µ = 8, what is the probability that x = 3?

P(3) ≈ (Round to four decimal places as needed)

    1. Perform the indicated calculation.

= (Round to four decimal places as needed)

    1. A frequency distribution is shown below. Complete parts (a) through (d)

The number of televisions per household in a small town

Televisions      0          1          2          3

Households     26        448      730      1400

  1. Use the frequency distribution to construct a probability distribution

X                     P(x)
0
1
2
3
(Round to the nearest thousandth as needed)

  1. Graph the probability distribution using a histogram. Choose the correct graph of the distribution below.

Describe the histogram’s shape.  Choose the correct answer below.

  1. Skewed right
    B. Skewed left
    C. Symmetric
  2. Find the mean of the probability distribution
    µ = (round to the nearest tenth as needed)
    Find the variance of the probability distribution
    σ2 = (round to the nearest tenth as needed)
    Find the standard deviation of the probability distribution
    σ = (round to the nearest tenth as needed)

Interpret the results in the context of the real-life situation.

  1. The mean is 2.3, so the average household has about 3 television. The standard deviation is 0.6 of the households differ from the mean by no more that about 1 television
    A. The mean is 0.6, so the average household has about 1 television. The standard deviation is 0.8 of the households differ from the mean by no more that about 1 television
    B. The mean is 2.3, so the average household has about 2 television. The standard deviation is 0.8 of the households differ from the mean by no more that about 1 television
  2. The mean is 0.6, so the average household has about 1 television. The standard deviation is 2.3 of the households differ from the mean by no more that about 3 television
    1. In the general population, one woman in eight will develop breast cancer. Research has shown that 1 woman is 650 carries a mutation of the BRCA gene.  Nine out of 10 women with this mutation develop breast cancer. a. Find the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene.

The probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene is. (Round to one decimal place as needed)

  1. Find the probability that a randomly selected woman will carry the mutation of the BRCA gene and will develop breast cancer.

The probability that a randomly selected woman will carry the gene nutation and develop breast cancer is. (Round to four decimal places as needed)

  1. Are the events of carrying this mutation and developing breast cancer independent or dependent?
  2. Dependent
    B. Independent
    1. Students in a class take a quiz with eight questions. The number x of questions answered correctly can be approximated by the following probability distribution.  Complete parts (a) through (e)

X                     0          1          2          3          4          5          6          7          8

P(x)                 0.04     0.04     0.06     0.06     0.12     0.24     0.23     0.14     0.07

  1. Use the probability distribution to find the mean of the probability distribution
    µ= (Round to the nearest tenth as needed)
    b. Use the probability distribution to find the variance of the probability distribution
    σ2= (Round to the nearest tenth as needed)
    c. Use the probability distribution to find the standard deviation of the probability distribution
    2.0 (Round to the nearest tenth as needed)
    d. Use the probability distribution to find the expected value of the probability distribution
    4.9 (Round to the nearest tenth as needed)
    e. Interpret the results
  2. The expected number of questions answered correctly is 2.0 with a standard deviation of 4.9 questions.
    B. The expected number of questions answered correctly is 4 with a standard deviation of 2.0 questions.
    C. The expected number of questions answered correctly is 4.9 with a standard deviation of 0.04 questions.
    D. The expected number of questions answered correctly is 4.9 with a standard deviation of 2.0 questions.
    1. Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Randomly choosing a multiple of 5 between 21 and 49

The sample space is {}  (Use a comma to separate answers as needed.  Use ascending order)

There are outcome(s) in the sample space.

    1. Decide if the events shown in the Venn diagram are mutually exclusive.

Are the events mutually exclusive?

  1.  Yes
    B.  No
    1. Determine whether the random variable is discrete or continuous.
  1. The number of free-throw attempts before the first shot is made
    b. The weight of a T-bone steak
    c. The number of bald eagles in the country
    d. The number of points scored during a basketball game
    e. The number of hits to a website in a day

(a) Is the number of free-throw attempts before the first shot is made discrete or continuous?

  1. The random variable is continuous
    B, The random variable is discrete

(b) Is the weight of a T-bone steak discrete or continuous?

  1. The random variable is discrete
    B. The random variable is continuous

(c) Is the number of bald eagles in the country discrete or continuous?

  1. The random variable is discrete
    B. The random variable is continuous

(d) Is the number of points scored during a basketball game discrete or continuous?

  1. The random variable is discrete
    B. The random variable is continuous

(e) Is the number of hits to a website in a day discrete or continuous?

  1. The random variable is discrete
    B. The random variable is continuous
  2.  A survey asks 1100 workers: Has the economy forced you to reduce the amount of vacation you plan to take this year?” Fifty-six percent of those surveyed say they are reducing the amount of vacation.  Twenty workers participating in the survey are randomly selected.  The random variable represents the number of workers who are reducing the amount of vacation.  Decide whether the experiment is a binomial experiment.  If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.

Is the experiment a binomial experiment?

  1. Yes
    B. No

What is a success in this experiment?

  1.  Selecting a worker who is reducing the amount of vacation
    B.  Selecting a worker who is not reducing the amount of vacation
    C.  This is not a binomial experiment

Specify the value of n.  Select the correct choice and fill in any answer boxes in your choice

  1.  N=
    B. This is not a binomial experiment

Specify the value of p.  Select the correct choice below and fill in any answer boxes in your choice.

  1.  P= (Type an integer or a decimal)
    B.  This is not a binomial experiment

Specify the value of q.  Select the correct choice below and fill in any answer boxes in your choice.

  1.  Q= (Type an integer r a decimal)
    B.  This is not a binomial experiment

List the possible values of the random variable x

  1.  X=0, 1, 2,…, 20
    B.  X=1, 2, 3,…, 1100
    C.  1, 2,…, 20
    D.  This is not a binomial experiment
  2.  Determine whether the distribution is a discrete probability distribution.

Is the distribution a discrete probability distribution?  Why?  Choose the correct answer below.

  1.  Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive
    B.  No, because the total probability is not equal to 1
    C.  Yes, because the distribution is symmetric
    D.  No, because some of the probabilities have values greater than 1 or less than 0
  2.  The table below shows the results of a survey that asked 2872 people whether they are involved in any type of charity work. A person is selected at random from the sample.  Complete parts (a) through (e).

Frequency       Occasionally    Not at all         Total

Male                226                  455                  793                  1474
Female             206                  450                  742                  1398
Total                432                  905                  1535                2872

  1.  Find the probability that the person is frequently or occasionally involved in charity work

P(being frequently involved or being occasionally involved) =  (Round to the nearest thousandth as needed)
b.  Find the probability that the person is male or frequently involved in charity work

P(being male or being frequently involved) =
c.  Find the probability that the person is female or not involved in charity work at all

P(being female or not being involved) = 0.763 (Round to the nearest thousandth as needed)
d. Find the probability that the person is female or not frequently involved in charity work

P(being female or not being frequently involved) = (Round to the nearest thousandth as needed)
e.  Are the events “being female” and “being frequently involved in charity work” mutually exclusive?

  1.  No, because 206 females are frequently involved in charity work.
    B.  Yes, because no females are frequently involved in charity work.
    C.  Yes, because 206 females are frequently involved in charity work.
    D.  No, because no females are frequently involved in charity work.
  2.  For the given pair of events, classify the two events as independent or dependent.

Swimming all day at the beach
Getting a sunburn
Choose the correct answer below.

  1.  The two events are independent because the occurrence on one does not affect the probability of the occurrence of the other.
    B.  The two events are dependent because the occurrence of one does not affect the probability of the occurrence of the other.
    C.  The two events are independent because the occurrence of one affects the probability of the occurrence of the other.
    D.  The two events are dependent because the occurrence of one affects the probability of the occurrence of the other.
  2.  Outside a home, there is a 9-key keypad with letters A, B, C, D, E, F, G, H, and I that can be used to open the garage if the correct nine-letter code is entered. Each key may be used only once.  How many codes are possible?

The number of possible codes is.

  1.  Determine the number of outcomes in the event. Decide whether the event is a simple event or not.

A computer is used to select randomly a number between 1 and 9, inclusive.  Event C is selecting a number less than 5.

Event has outcome(s)
Is the event a simple event?

1.Decide whether the random variable x is discrete or continuous
X represents the number of home theater systems sold per month at an electronics store.

1.Evaluate the given expression and express the results using the usual format for writing numbers (instead of scientific notation
36C2

2.Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.
N = 80, p = 0.4

2.Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.
N = 128, p = 0.36

    1. A new phone answering system for a company is capable of handling four calls every 10 minutes. Prior to installing the new system, company analysts determined that the incoming calls to the system are Poisson distributed with a mean equal to one every 10 minutes. If this incoming call distribution is what the analysts think it is, what is the probability that in a 10 – minute period more calls will arrive than the system can handle?

3.Suppose 90% of kids who visit a doctor have a fever, and 35% of kids with a fever have sore throats. What’s the probability that a kid who goes to the doctor has a fever and a sore throat?

    1. You randomly select one card from a standard deck. Event A is selecting a nine. Determine the number of outcomes in event A. then decide whether the event is a simple event or not.

4.A frequency distribution is shown below. Complete parts (a) through €.
The number of dogs per household in a small town.

Dogs012345
Households1295416163472712

5.22% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of students who say they use credit cards because of the rewards program is (a) exactly two, (b) more than two, and (c) between two and five inclusive. If convenient, use technology to find the probabilities.

5.The table below shows the results of a survey that asked 2870 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts (a) through (e).

6.The table below shows the results of a survey that asked 2885 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts (a) through (e).

6.Identify the sample space of the probability experiment and determine the number of outcomes in a sample space.
Randomly choosing an even number between 10 and 20, inclusive.

7.Students in a class take a math quiz with eight questions. The number x of questions answered correctly can be approximated by the following probability distributions. Complete parts (a) through €

7.Determine whether the events E and F are independent or dependent. Justify your answer.

8.A certain lottery has 29 numbers. In how many different ways can 4 of the numbers be selected? (assume that order of selection is not important.)

8.Determine the required value of the missing probability to make the distribution a discrete probability distribution

9.Determine whether the distribution Is a discrete probability distribution.

9.The histogram shows the distribution of stops for red traffic lights a commuter must pass through on her way to work. Use the histogram to find the mean, variance, standard deviation, and expected value of the probability distribution.

Statistics for Decision Making

10.Decide if the events are mutually exclusive.
Event A: Randomly selecting someone who is married
Event B: Randomly selecting someone who is a bachelor

10.A standard deck of cards contains 52 cards. One card is selected from the deck.
A)  compute the probability of randomly selecting a six or three.
B) compute the probability of randomly selecting a six, three, or king.
C) compute the probability of randomly selecting an eight or club.

11.A survey asks 1200 workers, “has the economy forced you to reduce the amount of vacation you plan to take this year?” 52% of those surveyed say they are reducing the amount of vacation. Ten workers participating in the survey are randomly selected. The random variable represents the number of workers who are reducing the amount of vacation. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p and q.

11.A study found that 36% of the assisted reproductive technology (ART) cycles resulted in pregnancies. Twenty eight percent of the ART pregnancies resulted in multiple births.

12.Use the bar graph below, which shows the highest level of education received by employees of a company, to find the probability that the highest level of education for an employee chosen random is E.

12.A golf-course architect has four linden trees, five white birch trees, and two bald cypress tress in a row along a fairway. In how many ways can the landscaper plant the trees in a row, assuming that the trees are evenly spaced?

13.Identify the sample space of the probability experiment and determine the number of outcomes in the sample space.

13.Decide if the events are mutually exclusive.
Event A) Receiving a phone call from someone who opposes all cloning
Event B) Receiving a phone call from someone who approves of cloning sheep.

14.Determine whether the events E and F are independent or dependent. Justify your answer.

14.47% of men consider themselves a professional baseball fan. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability tha the number who consider themselves baseball fans is (a) 8, (b) at least 8, and (c) less than eight. If convenient, use technology to find the probabilities.

15.Suppose 60% of kids who visit a doctor have a fever, and 30% of kids with a fever have sore throats. What’s the probability that a kid who goes to the doctor has a fever and a sore throat?

15.Given that x has a Poisson distribution with ᶙ = 8, what is the probability that x = 1?

16.Perform the indicated calculation.

Statistics for Decision Making

16.Use the frequency distribution, which shows the responses of a survey of college students when asked, “how often do you wear a seat belt when riding a car driven by someone else?” find the following probabilities of responses of college students from the survey chosen at random.

17.A frequency distribution is shown below. Complete parts (a) through (d).
The number of televisions per household in a small town.

Televisions0123
Households24437231409

17.About 30% of babies born with a certain ailment recover fully. A hospital is caring for six babies born with this ailment. The random variable represents the number of babies that recover fully.  Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.

18.A study found that 37% of the assisted reproductive technology (ART) cycles resulted in pregnancies. 24% of the ART pregnancies resulted in multiple births.
A) find the probability that a random selected ART cycle resulted in a pregnancy and produced a multiple birth.
B) find the probability that a randomly selected ART cycle that resulted in a pregnancy did not produce a multiple birth.
C) would it be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple birth?

    1. You randomly select one card from a standard deck. Event A is selecting a three. Determine the number of outcomes in event A. then decide whether the event is a simple event or not.

19.A company that makes cartons finds the probability of producing a carton with a puncture is 0.07, the probability that a carton has a smashed corner is 0.1, and the probability that a carton has a puncture and has a smashed corner is 0.007. answer parts (a) and (b)

19.Determine whether the random variable is discrete or continuous.
a. the # of bald eagles in the country.
b. the weight of a t-bone steak.
c. the time it takes for a light bulb to burn out.
d. the number of fish caught during a fishing tournament.
e. the distance a baseball travels in the air after being hit.

Statistics for Decision Making

Quiz Week 7 Recent

https://www.hiqualitytutorials.com/product/quiz-week-7-recent/

  1. A researcher wishes to​ estimate, with 90​% confidence, the population proportion of adults who say chocolate is their favorite ice cream flavor. Her estimate must be accurate within 4​% of the population proportion.

​(a) No preliminary estimate is available. Find the minimum sample size needed.

​(b) Find the minimum sample size​ needed, using a prior study that found that 44​% of the respondents said their favorite flavor of ice cream is chocolate.

​(c) Compare the results from parts​ (a) and​ (b).

A =
B =
C = Having an estimate of the population proportion…

  1. A doctor wants to estimate the HDL cholesterol of all 20-29 year old females. how many subjects are needed to estimate the HDL cholesterol within 4 points with 99% confidence assuming o = 16.1? suppose the doctor would be content with 95% confidence, how does the decrease in confidence affect the sample size required?

99% =
95 =
How does the decrease in confidence affect the sample size required? =…

  1. Construct the indicated confidence interval for the population mean μ using the​ t-distribution.
  1. 4. Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph. Assume the variable x is normally distributed.

The probability that the member selected is…

  1. 5. You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Which interval is​wider? If​convenient, use technology to construct the confidence intervals.

A random sample of 41 gas grills has a mean price of $644.50 Assume the population standard deviation is $55.40.

The 90% confidence interval is
The 95% confidence interval is

  1. 6. A manufacturer claims that the life span of its tires is 51,000 You work for a consumer protection agency and you are testing these tires. Assume the life spans of the tires are normally distributed. You select 100 tires at random and test them. The mean life span is 50,740 miles. Assume σ=900900.

Complete parts​ (a) through​ (c).

  1. 7. Use the normal distribution of SAT critical reading scores for which the mean is 502 and the standard deviation is 118.
  1. The table to the right shows the results of a survey in which 400 adults from the​ East, 400 adults from the​ South, 400 adults from the​ Midwest, and 400 adults from the West were asked if traffic congestion is a serious problem. Complete parts​ (a) and​ (b).

Construct a 99% confidence interval for the proportion of adults from the Midwest who say traffic congestion is a serious problem

Construct a 99% confidence interval for the proportion of adults from the West who say traffic congestion is a serious problem. Is it possible that these two proportions are equal?  Explain your reasoning

  1. 9. Find the probability and interpret the results. If​ convenient, use technology to find the probability. The population mean annual salary for environmental compliance specialists is about $65,500. A random sample of 31 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $62,500​? Assume σ=​$6,400.

Probability =…

  1. 10. Assume the random variable x is normally distributed with mean μ=88 and standard deviation σ=4.

Find the indicated probability.

​P(x < than<86​)

P(x <86​)=

Statistics for Decision Making

  1. 11. A vending machine dispenses coffee into a twelve​-ounce The amount of coffee dispensed into the cup is normally distributed with a standard deviation of 0.04 ounce. You can allow the cup to overfill 2% of the time. What amount should you set as the mean amount of coffee to be​ dispensed?
  2. 12. The time spent​ (in days) waiting for a kidney transplant for people ages​ 35-49 can be approximiated by the normal​ distribution, as shown in the figure to the right.

​(a) What waiting time represents the 99th percentile?

​(b) What waiting time represents the first​ quartile?

  1. 13. A population has a mean μ=7979 and a standard deviation σ=1818.

Find the mean and standard deviation of a sampling distribution of sample means with sample size

n=3636.

  1. 14. In a random sample of 35 refrigerators, the mean repair cost was $119.00 and the population standard deviation is $15.10. Construct a 95​% confidence interval for the population mean repair cost. Interpret the results.

95% confidence =
With 95% confidence…

  1. 15. In a survey of 7000 women, 4431 say they change their nail polish once a week. Construct a 99% confidence interval for the population proportion of women who change their nail polish once a week.

99% confidence =…

  1. 16. In a recent​ year, the scores for the reading portion of a test were normally​ distributed, with a mean of 3 and a standard deviation of 6.9.

Complete parts​ (a) through​ (d) below.

A =
B =
C =
D = The…

  1. 17. In a random sample of 21 people, the mean commute time to work was 7 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a​ t-distribution to construct a 95​% confidence interval for the population mean μ. What is the margin of error of μ​? Interpret the results.

U =
Margin of error =
With 95% confidence…

  1. 18. In a survey of 661 males ages​ 18-64, 397 say they have gone to the dentist in the past year. Construct​ 90% and​ 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. If​ convenient, use technology to construct the confidence intervals.

90% =
95% =
B =

Find the area of the indicated region under the standard normal curve.

Statistics for Decision Making

Quiz Week 7

https://www.hiqualitytutorials.com/product/math221-quiz-week-7/

    1. A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 35,000 miles and a standard deviation of 2800 miles. He wants to give a guarantee for free replacement of tires that don’t wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires?

Tires that wear out by …miles will be replaced free of charge.

    1. Find the indicated z-score shown in the graph to the right.

The z-score is

    1. A researcher wishes to estimate, with 95% confidence, the amount of adults who have high-speed internet access. Her estimate must be accurate within 4% of the true proportion.
      a) find the minimum sample size needed, using a prior study that found that 32% of the respondents said they have high-speed internet access(b) no preliminary estimate is available. Find the minimum sample size needed.a) =
      b) =
    2. The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of 221 milligrams per deciliter and a standard deviation of 37.7 milligrams per deciliter.
      (a) what percent of men have a total cholesterol level less than 228 milligrams per deciliter of blood?
      (b) if 251 men in the 35-44 age group are randomly selected, about how many would you expect to have a total cholesterol level greater than 264 milligrams per deciliter of blood?
      a) =
      b) =
    3. Find the z-score that has a 12.1% of the distribution’s area to it’s left.
      Answer =
    4. A doctor wants to estimate the HDL cholesterol of all 20-29 year old females. How many subjects are needed to estimate the HDL cholesterol within 2 points with 99% confidence assuming σ = 18.1? suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size required?
      99% =
      90% =
      how does the decrease in confidence affect the sample size required?
      Answer:
    5. Use a table of cumulative areas under the normal curve to find the z-score that corresponds to the given cumulative area. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores. If convenient, use technology to find the z-score. 0.054
      Answer:
    6. In a survey of 3076 adults, 1492 say they have started paying bills online in the last year.
      Construct a 99% confidence interval for the population proportion. Interpret the results.
      Answer:
      With 99% confidence, it can be said that the…
    7. Assume the random variable x is normally distributed with mean u = 89 and standard deviation o = 4. Find the indicated probability. P(76<x<82)
      Answer:
    1. Find the margin of error for the given values of c,s, and n.
      c = .90, s = 3.1, n =49
      Answer:
    1. Find the critical value Tc for the confidence level c = .90 and sample size n = 29.
      Tc =
    2. The mean height of women in a country (ages 20-29) is 63.9 inches. A random sample of 65 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume o = 2.91
      Answer =
    1. A survey was conducted to measure the height of men. In the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed with a mean of 67.9 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts (A) through (C).
      (a) the probability that his height is less than 68 inches.
      Answer:
      (b) the probability that his height is between 68-71 inches.
      Answer:
      (c) the probability that his height is more than 71 inches.
      Answer:
    1. For the standard normal distribution shown on the right, find the probability of z occurring in the region.Probability =
    1. Find the indicated probability using the standard normal distribution.
      (P – 1.35 < z < 1.35) =
    1. Find the margin of error for the given values of c, s, n.
      c = 0.98, s = 5, n = 6
      Answer:
    1. The systolic blood pressures of a sample of adults are normally distributed with a mean pressure of 115 millimeters of mercury and a standard deviation of 3.6 millimeters of mercury. The systolic blood pressures of four adults selected at random are 122 millimeters of mercury, 113 millimeters of mercury, 106 millimeters of mercury, and 128 millimeters of mercury. The graph of the standard normal distribution is below. Complete parts a – c.

(a) Match the values with the letters a/b/c/d.
A =
B =
C =
D =
(b) Find the z-scores that corresponds to each value
A =
B =
C =
D =

(c) Determine if any of the values are unusual, and classify them as either unusual or very unusual.

Answer: The unusual value(s) is

    1. You are given a sample mean and standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals. A random sample of 60 home theater systems has a mean price of $134.00 and a standard deviation is $19.60The 90% confidence interval is
      The 95% confidence interval isInterpret the results.

Answer: With 90% confidence, it can be…

    1. The monthly incomes for 12 randomly select people, each with a bachelor’s degree in economics, are shown on the right. Assume the population is normally distributed.

Mean =
Standard Deviation =
99% confidence interval =

    1. What is the total area under the normal curve?
      Answer =
    2. A population has a mean u = 82 and a standard deviation o = 36. Find the mean and standard deviation of a sampling distribution of sample means with sample size n = 81

Statistics for Decision Making

  1.  The amounts of time employees at a large corporation work each day are normally distributed, with a mean of 7.4 hours and a standard deviation of 0.38 hour. Random sample of size 25 and 37 are drawn from the population and the mean of each sample is determined. What happens to the mean and the standard deviation of the distribution of sample means as the size of the sample increases?

Mean of distribution =
Standard deviation of distribution =

If the sample size is n = 37, find the mean and standard deviation.

Mean =
Standard deviation =

What happens to the mean and standard deviation of the distribution of sample means as the size of the sample increases?
Answer: The mean stays the same, the but standard deviation decreases.

  1.  Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph.

1.Find the probability and interpret the results. If convenient, use technology to find the probability.

The population mean annual salary for environmental compliance specialist is about $64,000. A random sample of 35 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $62,000? Assume σ = $5,700

1.Use the standard normal table to find the z-score that corresponds to the cumulative area 0.1084. if the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z scores.

1.In a survey of women in a certain country (ages 20-29), the mean height was 63.8 inches with a standard deviation of 2.94 inches. Answer the following questions about the specified normal distribution.
A) what height represents the 99th percentile?
B) what height represents the first quartile?

2.Find the probability and interpret the results. If convenient, use technology to find the probability.
The population mean annual salary for environmental compliance specialists is about $61,000. A random sample of 42 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $57,500? Assume σ = $6,000

2.Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph. Assume the variable x is normally distributed.

    1. In a recent year, scores on a standardized test for high school students with a 3.50 – 4.00 GPA were normally distributed with a mean of 39.3 and a standard deviation of 2.3. A student with a 3.50 – 4.00 GPA who took the standardized test Is randomly selected.
    2. Find the z-scores for which 5% of the distribution area lies between –z and z.
    3. Use the central time limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution.
      The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 106 pounds and a standard deviation of 39.7 pounds. Random samples of size 19 are drawn from this population and the mean of each sample is determined.
    4. The mean height of women in a country (ages 20-29) is 64.2 inches. A random sample of 70 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume σ = 2.94
    5. The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of 202 milligrams per deciliter and a standard deviation of 37.6 milligrams per deciliter.

Answers:
A) The % of the men that have a total cholesterol level less than 213 milligrams per deciliter of blood is B) of the 259 men… would be expected to have a total cholesterol level greater 257 milligrams per deciliter of blood.

5.A researcher wishes to estimate, with 95% confidence, the proportion of adults who have high-speed internet access. Her estimate must be accurate within 2% of the true proportion.

Answers:

A – What is the minimum sample size needed using a prior study that found that 52% of the respondents said they have high-speed internet access? =
B – Minimum sample size needed? =5.

Find the margin of error for the given clues of c,s, and n.
c = 0.95, s = 2.7, n = 36

5.If a z-score is zero, which of the following is true?
5.Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected is from the shaded area.

6.Find the z-score that has 2.5% of the distribution area to it’s right.

6.Find the z-score that has 28.1% of the distribution’s area to its left

7.Find the margin of error for the given values of c,s, and n.
C = 0.95, s = 3.1, N = 100

    1. Find the critical value Tc for the confidence level c = 0.90 and sample size of n = 17
    2. In a survey of women in a certain country (ages 20-29) the mean height was 64.1 inches with a standard deviation of 2.94 inches. Answer the following questions about the specified normal distribution
      A) what height represents the 98th percentile?
      B) what height represents the first quartile

8.The SAT is an exam used by colleges and universities to evaluate the undergraduate applicants. The test scores are normally distributed. In a recent year, the mean test score was 1510 and the standard deviation was 315. The test scores of 4 random students are as follows: 1946, 1266, 2199, and 1407

(A) Without converting to z-scores, match the values with the letters a/b/c/d on the given graph of the standard normal distribution.
(B) Find the z-scores that corresponds to each value
C) Determine whether any of the values are unusual.
Answer: The unusual value(s) is/are

    1. A beverage company uses a machine to fill one-liter bottles with water. Assume that the population of volumes is normally distributed. (a) the company wants to estimate the mean value of water the machine is putting in the bottles within 1 milliliter. Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 4 milliliters.
      (b) Repeat part (a) using an error tolerance of 3 milliliters. Which error tolerance requires a larger sample size?

Answers:
(A) the minimum sample size required for an error tolerance of 1 is… bottles
(b) the minimum sample size required for an error tolerance of 3 is …bottles

The error tolerance of … requires a larger sample size. As the error size decreases, a larger sample must be taken to obtain sufficient information from the population to ensure accuracy.

    1. A population has a mean u = 83 and a standard deviation o = 23. Find the mean and standard deviation of sample means with sample size n = 247.
      Answer
    2. The monthly income for 12 randomly selected people, each with a bachelor’s degree in economics, are shown on the right. Assume the population is normally distributed.

9.Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph.

    1. Find the indicated probability using standard normal distribution.
      P(-0.78 < Z < 0.78)
      10.Use the normal distribution of fish lengths for which the mean is 11 inches and the standard deviation is 5 inches. Assume the variable x is normally distributed.
      (a) what percent of fish are longer than 13 inches?
      (b) if 500 fish are randomly selected, how many would be shorter than 9 inches?
    2. Find the margin of error for the given values of c,s, and n.
      C = 0.90, s = 3.2, n =100
    3. A researcher wishes to estimate, with 90% confidence, the proportion of adults who have high-speed internet access. Her estimate must be accurate within 4% of the true proportion.
      A – Find the minimum sample size needed using a study of 46%
      B – No estimate is available. Find the minimum sample size.

11.A doctor wants to estimate the HDL cholesterol of all 20-29 year old females. How many subjects are needed to estimate the HDL cholesterol within 2 points with 99% confidence assuming o = 17.3? suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size?

11.The systolic blood pressures of a sample of adults are normally distributed, with a mean pressure of 115 millimeters of mercury and a standard deviation of 3.6 millimeters of mercury. The systolic blood pressures of four adults selected at random are 121 millimeters of mercury, 114 millimeters of mercury, 105 millimeters of mercury, and 126 millimeters of mercury. The graph of the standard normal distribution is shown to the right. Complete parts (a) through (c) below.

a….

b….

Statistics for Decision Making

    1. The unusual value(s) is/are …. The very unsual(s) is/are …
    2. In a recent year, scores on a standardized test for high school students with a 3.50 to 4.00 gpa were normally distributed, with a mean of 39.7 and a standard deviation of 2.5. A student with a 3.50 to 4.00 gpa who took the standardized test is randomly selected.A. find the probability that the student’s test score is less than 35.
      B. find the probability that the student’s test score is between 35.7 and 43.7
      C. find the probability that the student’s test score is more than 41.7
    3. Find the margin of error for the given values of c,s, and n.
      C = 0.95, S = 4, N = 27
    4. Assume the random variable x is normally distributed with mean u = 50 and standard deviation o = 7. Find the indicated probability. P(X>39)
      12. The systolic blood pressures of a sample of adults are normally distributed, with a mean pressure of 115 millimeters of mercury and a standard deviation of 3.6 millimeters of mercury. The systolic blood pressures of four adults selected at random are 119 millimeters of mercury, 113 millimeters of mercury, and 127 millimeters of mercury. The graph of the standard normal distribution is shown to the right. Complete parts (a) through (c) below.
    • Without converting to z-scores, match the values with the letters A, B, V, and D on the given graph above of the standard normal distribution.
    • Find the z-score that corresponds to each value and check your answers to part (a)
    • Determine whether any of the values are unusual, and classify them as either unusual or very unusual. Select the correct answer below and, if necessary, fill in the answer box(es) within your choice….
    1. Use a table of cumulative areas under the normal curve to find the z-score that corresponds to the given cumulative area. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between corresponding z-scores. If convenient, use technology to find the z-score. 0.049.
    2. Find the critical value t for the confidence level c =0.99 and sample size n = 13.

Click the icon to view the t-distribution table.

    1. Find the margin of terror for the given values of c,s, and n.
      C = 0.95, S = 3.9, N = 26

14 For the standard normal distribution shown on the right, find the probability of z occurring in the indicated region. -0.62

Answer =

    1. You are given the sample mean and sample and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals.

A random sample of 36 gas grills has a mean price of $637.60 and a standard deviation of $55.80

14.Use the central limit theorem to find the mean and the standard error of the mean of the indicated sampling distribution. The sketch a graph of the sampling distribution.

The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 113 pounds and a standard deviation of 39.1 pounds. Random samples of size 18 are drawn from this population and the mean of each sample is determined.

    1. What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?

15.Find the indicated probability using the standard normal distribution.
P (-0.21 < z < 0.21)

    1. You are given the sample mean and the sample standard deviation. Use this information to construct 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct confidence intervals.
      A random sample of 40 home theater systems has a mean price of $1111.00 and a standard deviation is $15.50
    2. A population has a mean u = 80 and a standard deviation o = 30. Find the mean and standard deviation of a sampling distribution of sample means with sample size 250.
    3. The monthly incomes for 12 randomly selected people, each with a bachelor’s degree in economics, are shown above. Assume the population is normally distributed.

16.A population has a mean of 75 and standard deviation of 36. Find the mean/sd of a sampling distribution of sample means with sample size n = 81.

Mean = 75
Standard deviation = 4

17.Find the indicated probability using the standard normal distribution.
P ( -0.37 < z < 0.37)
17. Find the indicated z-scores shown in the graph.

    1. In a survey of 3455 adults, 1467 say they have started paying bills online in the last year.
      Construct a 99% confidence interval for the population proportion. Interpret the results.

18.The amounts of time employees at a large corporation work each day are normally distributed, with a mean of 7.8 hours and a standard deviation of 0.33 hour. Random sample of size 25 and 38 are drawn from the population and the mean of each sample is determined. What happens to the mean and the standard deviation of the distribution of sample means as the size of the sample increases?

If the sample size n = 25, find the mean and standard deviation of the distribution of sample means.

    1. Find the margin of error for the given values of c,s, and n.
      C = 0.98, s = 5, n = 24
    2. A researcher wishes to estimate, with 99% confidence, the proportion of adults who have high-speed internet access. Her estimate must be accurate within 4% of the true proportion.
      A) find the minimum sample size needed, using a prior study that found that 54% of the respondents said that they have high speed internet access.
      B) no preliminary estimate is available. Find the minimum sample size needed.

19.In a survey of women in a certain country (ages 20-29), the mean height was 63.4 inches with a standard deviation of 2.87 inches. Answer the following questions about the specified normal distribution.
A) what height represents the 95th percentile?
B) what height represents the first quartile

    1. In a normal distribution, which is greater, the mean or the median?

Find the indicated z-score shown in the graph

    1. In a normal distribution, which is greater, the mean or the median? Explain.
      20. You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider?
      A random sample of 31 gas grills has a mean price of $631.70 and a standard deviation of $55.10
    2. The monthly incomes for 12 randomly selected people, each with a bachelor’s degree in economics, are shown on the right. Assume the population is normally distributed.
    3. A beverage company uses a machine to fill cone-liter bottles (see figure). Assume that the population of volumes is normally distributed.

(a) The company wants to estimate the mean volume of water the machine is putting in the bottles within 1 milliliter.  Determine the minimum sample size required to construct a 95% confidence interval for the population mean.  Assume the population standard deviation is 3 milliliters.
(b) Repeat part (a) using an error tolerance of 2 milliliters.  Which error tolerance requires a larger sample size?  Explain.

    1. Find the standard normal distribution show on the right, find the probability of z occurring in the indicated region.
    1. Assume the random variable x is normally distributed with mean = 50 and standard deviation = 7. P (X>35)

Answer =

Statistics for Decision Making

21.In a survey of 3068 adults, 1462 say they have started paying bills online in the last year.  Construct a 99% confidence interval for the population proportion.  Interpret the results.  Choose the correct answer below…

    1. Use a table of cumulative areas under the normal curve to find the z-score that corresponds to the given cumulative area. If the area is not in the table, use the try closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores. If convenient, use technology to find the z-score. 0.051.

Answer =

    1. In a survey of 640 male ages 18-64, 392 say they have gone to the dentist in the past year. Construct a 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the confidence intervals. If convenient, use technology to construct the confidence intervals.

The 90% confidence interval is 0.580, 0.644
The 95% confidence interval is 0.575, 0650
With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.

    1. Find the critical value Tc for the confidence level c = 0.80 and sample size n = 14.

Tc = 1.350

    1. Assume the random variable x is normally distributed with mean u = 50 and standard deviation = 7. P ( X > 38)
      23. For the standard normal distribution shown on the right, find the probability in the indicated region.

23.The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of 206 milligrams per deciliter and a standard deviation of 37.6 milligrams per deciliter.
A) what % of the men have a total cholesterol level less than 240 milligrams per deciliter of blood?
B) if 240 men in the 35-44 age group are randomly selected, about how many would you expect to have total cholesterol level greater than 252 milligrams per deciliter of blood?

Statistics for Decision Making

Homework Week 1

https://www.hiqualitytutorials.com/product/math221-homework-week-1/

1  Determine whether the data set is a population or a sample. Explain your reasoning.

The age of each resident in an apartment building.

1  Determine whether the data set is a population or a sample. Explain your reasoning.

The salary of each baseball player in a league

  1. Determine whether the data set is a population or a sample. The number of restaurants in each city in a state.

2  Determine whether the underlined value is a parameter or a statistic.

The average age of men who have walked on the moon was 39 years, 11 months, 15 days.

Is the value a parameter or a statistic?

2  Determine whether the data set is a population or a sample.  Explain your reasoning.

The number of pets for 20 households in a town of 300 households.

Choose the correct answer below.

  1. Determine whether the data is a population or sample. The age of one person per row in a cinema.

3  Determine whether the given value is a statistic or a parameter.

In a study of all 3336 professors at a college, it is found that 55% own a vehicle.

3  Determine whether the underlined value is a parameter or a statistic.

In a national survey of high school students (grades 9-12), 25% or respondents reported that someone had offered, sold, or given them an illegal drug on school property.

  1. Determine whether the underlined value is a parameter or a statistic.
    The average age of men who have walked on the moon was 39 years, 11 months, 15 days.

4  Determine whether the given value is a statistic or a parameter.

In a study of all 4901 professors at a college, it is found that 35% own a television.

4  Determine whether the given value is a parameter or a statistic.

In a study of all 1290 employees at a college, it is found that 40% own a computer.

  1. Determine whether the given value is a statistic or a parameter.
    A sample of professors is selected and it is found that 65% own a television.
    5  Determine whether the variable is qualitative or quantitative.

Favorite film Is the variable qualitative or quantitative?

5  Determine whether the given value is a statistic or a parameter.

A sample of employees is selected and it is found that 45% own a vehicle.

  1. Determine whether the given value is a statistic or a parameter.
    A sample of seniors is selected and it is found that 65% own a computer.

6  Determine whether the variable is qualitative or quantitative.

Hair color Is the variable qualitative or quantitative?

6  Determine whether the variable is qualitative or quantitative.

Favorite sport Is the variable qualitative or quantitative?

  1. Determine whether the variable is qualitative or quantitative
    Favorite Film

7  The regions of a country with the six highest per capital incomes last year are shown below.

  1. Southeast Western  3 Eastern  4 Northeast  5 Southeast   6 Northern

Determine whether the data are qualitative or quantitative and identify the data set’s level of measurement.  What is the data set’s level of measurement?

  1.  Ratio B.  Ordinal C.  Interval  D. Nominal

7  Determine whether the variable is qualitative or quantitative.

Car license  Is the variable Quantitative?

7.Determine whether the variable is qualitative or quantitative
Gallons of water in a swimming pool

8  Which method of data collection should be used to collect data for the following study.  The average age of the 105 residents of a retirement community.

8  The region representing the top salesperson is a corporation for the past six years is shown below.

Northern          Northern          Eastern                        Southeast        Eastern                        Northern

Determine whether the data are qualitative or quantitative and identify the data set’s level of measurement.  Are the data qualitative or quantitative?  What is the data set’s level of measurement?

  1. The region of a country with the longest life expectancy for the past six years is shown below.

Western, Southeast, Southwest, Northeast, Northeast, Southeast,

9  Decide which method of data collection you would use to collect data for the study.

A study of the effect on the taste of a popular soda made with a caffeine substitute.

9  Which method of data collection should be used to collect data for the following study.

The average weight of 188 students in a high school.

  1. Which method of data collection should be used to collect data for the following study.
    The average age of 124 residents of a retirement community

10  Microsoft wants to administer a satisfaction survey to its customers. Using their customer database, the company randomly selects 60 customers and asks them about their level of satisfaction with the company.  What type of sampling is used?

10 Decide which method of data collection you would use to collect data for the study.

A study of the effect on the human digestive system of a snack food made with a sugar substitute.

  1. Decide which method of data collection you would use to collect data for the study.
    A study of the effect on human digestive system of a snack food made with a fat substitute.
    11  A newspaper asks its readers to call in their opinion regarding the number of books they have read this month. What type sampling is used?

11  General Motors wants to administer a satisfaction survey to its current customers.  Using their customer database, the company randomly selects 80 customers and asks them about their level of satisfaction with the company.  What type of sampling is used?

12  Determine whether you would take a census or a sampling to collect data for the study described below.

The most popular chain restaurant among the 60,000 employees of a company.  Would you take a census or use a sampling?

  1. Sony wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 50 customers and asks them about what their level of satisfaction with the company.
    12  A magazine asks its readers to call in their opinion regarding the quality of the articles. What type of sampling is used?
  2. A television station asks its viewers to call in their opinion regarding the desirability of programs in high definition TV.

13  Math the plot with a possible description of the sample.

Choose the correct answer below.

  1.  Top speeds (in miles per hour) of a sample of sports cars
  2.  Time (in minutes) it takes a sample of employees to drive to work
  3.  Grade point averages of a sample of students with finance majors
  4.  Ages (in years) of a sample of residents of a retirement home

13  Determine whether you would take a census or use a sampling to collect data for the study described below.

The most popular house color among the 40,000 employees of a company.  Would you take a census or use a sampling?

  1. Determine whether you would take a census or use a sampling to collect data for the study described below. The most popular chain restaurant among the 35 employees of a company.

14  Use a stem-and-leaf plot to display the data. The data represent the heights of eruptions by geyser.  What can you conclude about the data?

108                  90                    110                  150
140                  120                  100                  130
110                  100                  118                  106
98                    102                  105                  120
111                  130                  96                    124

Choose the correct stem-and-leaf plot. (Key: 15 ǀ 5 = 155)

What can you conclude about the data?

14  Match the plot with a possible description of the sample.

Choose the correct answer below.

  1.  Fastest serve (in miles per hour) of a sample of top tennis players
  2.  Grade point averages of a sample of students with finance major
  3.  Time (in minutes) it takes a sample of employees to drive to work
  4.  Ages (in years) of a sample of residents of a retirement home

14.Match the plot with a possible description of the sample.

15  Determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these.

Choose the best answer below.

  1.  Skewed right
  2.  Skewed left
  3.  Symmetric
  4.  Uniform
  5.  None of these

15  Use a stem-and-leaf plot to display the data.  The data represent the heights of eruptions by a geyser.  What can you conclude about the data?

106                  90                    110                  150
140                  120                  100                  130
110                  101                  115                  100
99                    107                  103                  120
115                  130                  95                    121

What can you conclude about the data?

16  The maximum number of seats in a sample of 13 sport utility vehicles are listed below. Find the mean, median, and mode of the data.

5 7 8 8 5 6 4 4 4 4 4 4 5

Find the mean.  Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

  1.  The mean is

(Type the integer or decimal rounded to the nearest tenth as needed)

  1.  The data does not have a mean.

Find the median.  Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

  1.  The median is

(Type the integer or decimal rounded to the nearest tenth as needed)

  1.  The data does not have a median.

Find the mode.  Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

  1.  The median is

(Type the integer or decimal rounded to the nearest tenth as needed)

  1.  The data does not have a mode.

16  Determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of those.

Choose the best answer below.

  1.  Skewed right
  2.  Skewed left
  3.  Symmetric
  4.  Uniform
  5.  None of these

Determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these.

17  Find the range, mean, variance, and standard deviation of the sample data set.
14 12 13 8 20 7 18 16 15

The range is

17 The maximum number of seats in a sample of 13 sport utility vehicles are listed below.  Find the mean, median, and mode of the data.
8 10 11 11 8 7 7 7 9 7 7 7 8

Find the mean.  Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

  1.  The mean is

(Type the integer or decimal rounded to the nearest tenth as needed)

  1.  The data does not have a mean.

Find the median.  Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

  1.  The median is

(Type the integer or decimal rounded to the nearest tenth as needed)

  1.  The data does not have a median

Find the mode.  Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

  1.  The mode is

(Type the integer or decimal rounded to the nearest tenth as needed)

  1.  The data does not have a mode
  2. The maximum # of seats in a sample of 13 sport utility vehicles are listed below. Find the mean, median, and mode of the data. 8 8 11 11 8 7 7 7 9 7 7 7 10

Find the mean. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

18  The ages of 10 brides at their first marriage are given below.

35.9  32.6  28.7  37.7  44.7  31.3  29.5  23.2  22.4  33.6

(a) Find the range of the data set.
Range = (round to the nearest tenth as needed)
(b) Change 44.7 to 61.3 and find the range of the new data set.
Range = 38.9 (round to the nearest tenth as needed)
(c) Compare your answer to part (a) with your answer to part (b)

  1.  Changing the maximum value of the data set does not affect the range
  2.  Changing the minimum value of the data set does not affect the range
  3.  Changing the minimum value of the data set greatly affects the range
  4.  Changing the maximum value of the data set greatly affects the range

18  Find the range, mean, variance, and standard deviation of the sample data set.
10 14 13 5 19 11 18 12 9

The range is

  1. Find the range, mean, variance, and standard deviation of the sample data set.
    8 15 14 17 9 7 13 11 20

19  Heights of men on a baseball team have a bell-shaped distribution with a mean of 185 cm and a standard deviation of 6 cm. Using the empirical rule, what is the approximate percentage of the men between the following values?

  1.  173 cm and 197 cm
  2.  167 cm and 203 cm

A % of the men are between 173 cm and 197 cm
B % of the men are between 167 cm and 203 cm (Do not round)

19.The ages of 10 brides at their first marriage are given below.
24.4 31.8 35.8 32.5 44.2 24.5 26.2 24.6 22.5 27.2

20  The mean value of land and buildings per acre from a sample of farms is $1400, with a standard deviation of $100. The data set has a bell-shaped distribution.  Assume the number of farms in the sample is 70.

  1.  Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1300 and $1500.

farms (Round to the nearest whole number as needed)

  1.  If 28 additional farms were sampled, about how many of these additional farms would you expect to have land and building value between $1300 per acre and $1500 per acre?
  2. Heights of men on a baseball team have a bell-shaped distribution with a mean of 182 cm and a standard deviation of 6 cm. Using the empirical rule, what is the approximate percentage of the men between the following values?
    A. 170 cm and 194 cm
    B. 176 cm and 188 cm

Statistics for Decision Making

21   Use the box-and-whisker plot to identify

(a)  The minimum entry
(b)  The maximum entry
(c)  The first quartile
(d)  The second quartile
(e)  The third quartile
(f)  The interquartile range

(a)  Min =
(b)  Max =
(c)  Q 1 =
(d)  Q 2 =
(e)  Q 3 =
(f)  IQR =

19  The ages of 10 brides at their first marriage are given below
22.6  23.7  35.6  39.2  44.7  29.6  30.8  31.7  24.5  28.2

(a) Find the range of the data set
Range =

(b) Change 44.7 to 68.3 and find the range of the new data set
Range =

(c)  Compare your answer to part (a) with your answer to part (b).

  1.  Changing the maximum value of the data set greatly affects the range
  2.  Changing the minimum value of the data set greatly affects the range
  3.  Changing the maximum value of the data set does not affect the range
  4.  Changing the minimum value of the data set does not affect the range

20  Heights of men on a baseball team have a bell-shaped distribution with a mean of 172 cm and a standard deviation of 7 cm.  Using the empirical rule, what is the approximate percentage of the men between the following values?

  1.  151 cm and 193 cm
  2.  165 cm and 179 cm
  3.  % of the men are between 151 cm and 193 cm (Do not round)
  4.  % of the men are between 165 cm and 179 cm (Do not round)

20  The midpoints A, B, and C are marked on the histogram. Match them to the indicated scores.  Which scores, if any, would be considered unusual?

The point A corresponds with z = The point B corresponds with z =
The point C corresponds with z =
Which scores, if any, would be considered unusual?

  1.  41
  2.  -2.17
  3.  0
  4.  None

Homework Week 2

https://www.hiqualitytutorials.com/product/math221-homework-week-2/

    1. Two variables have a positive linear correlation. Does the dependent variable increase or decrease as the independent variable increases?
    2. Two variables have a positive linear correlation. Does the dependent variable increase or decrease as the independent variable increases?
    3. Discuss the difference between r and p

Choose the correct answers below.

R represents the sample correlation coefficient.
P represents the population correlation coefficient

    1. Discuss the difference between r and p.
    2. The scatter plot of a paired data set is shown. Determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables.

Choose the correct answer below.

  1.  no linear correlation
    B.  strong positive linear correlation
    C.  strong negative linear correlation
    D.  perfect negative linear correlation
    E.  perfect positive linear correlation

3   The scatter plot of a paired data set is shown.  Determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables.

    1. The scatter plot of a paired data set is shown. Determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables.

4  Identify the explanatory variable and the response variable.

A golfer wants to determine if the amount of practice every year can be used to predict the amount of improvement in his game.

4  Identify the explanatory variable and the response variable.

A teacher wants to determine if the amount of textbook used by her students can be used to predict the students’ test scores

4.Identify the explanatory variable and the response variable.
a golfer wants to determine if the amount of practice every year can be used to predict the amount of improvement in his game.

5   Two variables have a positive linear correlation. Is the slope of the regression line for the variables positive or negative?

5.Two variables have a positive linear correlation. Is the slope of the regression line for the variables positive or negative?

6  Given a set of data and a corresponding regression line, describe all values of x that provide meaningful predictions for y.

    1.  Prediction values are meaningful for all x-values that are realistic in the context of the original data set.
    2.  Prediction values are meaningful for all x-values that are not included in the original data set.
    3.  Prediction values are meaningful for all x-values in (or close to) the range of the original data.

Statistics for Decision Making

5.Two variables have a positive linear correlation. Is the slope of the regression line for the variables positive or negative?

7  Match this description with a description below.

The y-value of a data point corresponding to

Choose the correct answer below.

8  Match this description with a description below.

The y-value for a point on the regression line corresponding to

Choose the correct answer below.

    1. Match this description with a description below.
      the y-value of a data point corresponding to x

9  Match the description below with its symbol(s).

The mean of the y-values

Select the correct choice below.

10  Match the regression equation  with the appropriate graph.

Choose the correct answer below.

10  Match the regression equation with the appropriate graph.

11

    1. Match the regression equation y = 1.662x + 83.34 with the appropriate graph.

12  Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?

R= -0.312

Calculate the coefficient of determination

What does this tell you about the explained variation of the data about the regression line?
% of the variation can be explained by the regression line.  About the unexplained variation?
% of the variation is unexplained and is due to other factors or to sampling error.  (Round to three decimal places as needed)

12  Use the value of the linear correlation coefficient to calculate the coefficient of determination.  What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?

R= -0.324

Calculate the coefficient of determination

What does this tell you about the explained variation of the data about the regression line?
% of the variation can be explained by the regression line.  About the unexplained variation?
% of the variation is unexplained and is due to other factors or to sampling error.

12  Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?

R = 0.481

Calculate the coefficient of determination

What does this tell you about the explained variation of the data about the regression line?
% of the variation can be explained by the regression line.
% of the variation is unexplained and is due to other factors or to sampling error.

12  Use the value of the linear correlation coefficient to calculate the coefficient of determination.  What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?

R = 0.224

Calculate the coefficient of determination

What does this tell you about the explained variation of the data about the regression line?
% of the variation can be explained by the regression line.
% of the variation is unexplained and is due to other factors or to sampling error.

12  The equation used to predict college GPA (range 0-4.0) is

is high school GPA (range 0-4.0) and x2 is college board score (range 200-800). Use the multiple regression equation to predict college GPA for a high school GPA of 3.5 and college board score of 400.

The predicted college GOA for a high school GPA of 3.5 and college board of 400 is.  (Round to the nearest tenth as needed).

    1. Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? R = 0.862

13  Use the value of the linear correlation coefficient to calculate the coefficient of determination.  What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?

R = 0.909

Calculate the coefficient of determination

What does this tell you about the explained variation of the data about the regression line?
% of the variation can be explained by the regression line.
% of the variation is unexplained and is due to other factors or to sampling error.  (Round to three decimal places as needed)

13  The equation used to predict the total body weight (in pounds) of a female athlete at a certain school is the female athlete’s height (in inches) and x2 is the female athlete’s percent body fat. Use the multiple regression equation to predict the total body weight for a female athlete who is 64 inches tall and has 17% body fat.

The predicted total body weight for a female athlete who is 64 inches tall and has 17% body fat is pounds.

13.Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the about the regression line? About the unexplained variation? R = 0.592

14  The equation used to predict college GPA (range 0-4.0) is

high school GPA (range 0-4.0) and X2 is college board score (range 200-800). Use the multiple regression equation to predict college GPA for a high school GPA of 3.2 and a college board score of 500.

The predicted college GPA for a high school GPA of 3.2 and college board score of 500 is.

14.The equation used to predict college GPA (range 0-4.0) is y = 0.21 + 0.52x + 0.002x, where x is high school GPA (range 0-4.0) and x is college board score (range 200-800). Use the multiple regression equation to predict college gpa for a high school gpa of 3.2 and a college board score of 600.

15  The equation used to predict the total body weight (in pounds) of a female athlete at a certain school is  the female athlete’s height (in inches) and X2 is the female athlete’s percent body fat. Use the multiple regression equation to predict the total body weight for a female athlete who is 67 inches tall and has 24% body fat.

The predicted total body weight for a female athlete who is 67 inches tall and has 24% body fat is pounds.

15.The equation used to predict the total body weight of a female athlete at a certain school is y = -112 + 3.29x + 1.64x, where x is the female athlete’s height and x is the females athlete’s % body fat. Use the multiple regression equation to predict the total body weight for a female athlete who is 63 inches tall and has 19% body fat.

Statistics for Decision Making

MATH 221 Homework Week 3

https://www.hiqualitytutorials.com/product/math221-homework-week-3/

1  The access code for a car’s security system consist of four digits. The first digit cannot be zero and the last digit must be odd.  How many different codes are available?

 1  The access code for a car’s security system consist of four digits. The first digit cannot be 6 and the last digit must be even or zero.  How many different codes are available?

1.The access code for a car’s security system consists of four digits. The first digit cannot be 1 and must e even or 0. How many different codes are there?

2  A probability experiment consists of rolling a 6-sided die. Find the probability of the event below:

Rolling a number is less than 5

2  A probability experiment consists of rolling a 6-sided die. Find the probability of the event below:

Rolling a number is less than 4

  1. A probability experiment consists of rolling a 6-sided die. Find the probability of rolling a number less than 4.

3  Use the frequency distribution, which shows the responses of a survey of college students when asked, “How often do you wear a seat belt when riding in a car driven by someone else?” Find the following probabilities of responses of college students from the survey chosen at random.

Use the frequency distribution, which shows the responses of a survey of college students when asked, “how often do you wear a seat belt when riding in a car driven by someone else? Find the following probability of responses of college students from the survey chosen at random.

4  Determine whether the events E and F are independent or dependent. Justify your answer.

  1.  E: A person having an at-fault accident.

F: The same person being prone to road rage.

  1.  E and F are dependent because having an at-fault accident has no effect on the probability of a person being prone to road rage.
  2.  E and F are dependent because being prone to road rage can affect the probability of a person having an at-fault accident.
  3.  E and F are independent because having an at-fault accident has no effect on the probability of a person being prone to road rage.
  4.  E and F are independent because being prone to road rage has no effect on the probability of a person having an at-fault accident.
  5.  E: A randomly selected person accidentally killing a spider.

F: Another randomly selected person accidentally swallowing a spider.

  1.  E can affect the probability of F, even if the two people are randomly selected, so the events are dependent.
  2.  E can affect the probability of F because the people were randomly selected, so the events are dependent.
  3.  E cannot affect F and vice versa because the people were randomly selected, so the events are independent.
  4.  E cannot affect F because “person 1 accidentally killing a spider” could never occur, so the events are neither dependent nor independent.
  5.  E: The consumer demand for synthetic diamonds.

F: The amount of research funding for diamond synthesis.

  1.  The consumer demand for synthetic diamonds could not affect the amount of research funding for diamond synthesis, so E and F are independent.
  2.  The consumer demand for synthetic diamonds could affect the amount of research funding for diamond synthesis, so E and F are dependent.
  3.  The amount of research funding for diamond synthesis could affect the consumer demand for synthetic diamonds, so E and F are dependent.
  4.  E: The unusually foggy weather in London on May 8

F: The number of car accidents in London on May 8

  1.  The unusually foggy weather in London on May 8 could not affect the number of car accidents in London on May 8, so E and F are independent.
  2.  The number of car accidents in London on May 8 could affect the unusually foggy weather in London on May 8, so E and F are dependent
  3.  The unusually foggy weather in London on May 8 could affect the number of car accidents in London on May 8, so E and F are dependent
  4. Determine whether the events E and F are independent or dependent. Justify your answer.
    (a)
    E: A person having an at-fault accident
    F: The same person being prone to road rage

(b)
E: A randomly selected person accidentally killing a spider.
F: Another random person swallowing a spider

(c)
E: The consumer demand for synthetic diamonds
F: The amount of research funding for diamond synthesis

5  The table below shows the results of a survey in which 147 families were asked if they own a computer and if they will be taking a summer vacation this year.

Summer Vacation This Year
                                               Yes                 No                  Total
Own a             Yes                  46                    11                    57
Computer        No                   56                    34                    90
Total                                        102                  45                    147
  1.  Find the probability that a randomly selected family is not taking a summer vacation this year.
    The probability is (Round to the nearest thousandth as needed.)
    b.  Find the probability that a randomly selected family owns a computer.
    The probability is (Round to the nearest thousandth as needed.)
    c.  Find the probability that a randomly selected family is taking a summer vacation this year given that they own a computer.
    The probability is (Round to the nearest thousandth as needed.)
    d.  Find the probability that a randomly selected family is taking a summer vacation this year and owns a computer.
    The probability is (Round to the nearest thousandth as needed.)
    e.  Are the events of owning a computer and taking a summer vacation this year independent or dependent events?

6  The table below shows the results of a survey in which 147 families were asked if they own a computer and if they will be taking a summer vacation this year.

Summer Vacation This Year
Yes                  No                   Total
Own a             Yes                  47                    11                    58
Computer        No                   56                    33                    89
Total                                        103                  44                    147
  1.  Find the probability that a randomly selected family is not taking a summer vacation this year.

The probability is

  1.  Find the probability that a randomly selected family owns a computer.

The probability is

  1.  Find the probability that a randomly selected family is taking a summer vacation this year given that they own a computer.

The probability is

  1.  Find the probability that a randomly selected family is taking a summer vacation this year and owns a computer.

The probability is (Round to the nearest thousandth as needed.)

  1.  Are the events of owning a computer and taking a summer vacation this year independent or dependent events?
  2. The table below shows the results of a survey in which 146 families were asked if they own a computer and if they will be taking a summer vacation this year.(A) Find the probability that a random family is not taking a summer vacation this year.
    (B) Find the probability that a random family owns a computer
    (C) Find the probability that a random family is taking a vacation given that they own a computer
    (D) Find the probability that a random family is taking a vacation and own a computer.
    (E) Are the events of owning a computer and taking a vacation independent or dependent?6  The table below shows the results of a survey in which 147 families were asked if they own a computer and if they will be taking a summer vacation this year.
Summer Vacation This Year
Yes                  No                   Total
Own a             Yes                  47                    11                    58
Computer        No                   56                    33                    89
Total                                        103                  44                    147
    1. a.  Find the probability that a randomly selected family is not taking a summer vacation this year.

The probability is

    1.  Find the probability that a randomly selected family owns a computer.

The probability is

    1.  Find the probability that a randomly selected family is taking a summer vacation this year given that they own a computer.

The probability is

    1.  Find the probability that a randomly selected family is taking a summer vacation this year and owns a computer.

The probability is

    1.  Are the events of owning a computer and taking a summer vacation this year independent or dependent events?

Statistics for Decision Making

7  A distribution center receives shipments of a product from three different factories in the quantities of 50, 30, and 20. Three times a product is selected at random, each time without replacement.  Find the probability that (a) all three products came from the second factory and (b) none of the three products came from the second factory.

7  A distribution center receives shipments of a product from three different factories in the quantities of 50, 30, and 20. Three times a product is selected at random, each time without replacement.  Find the probability that (a) all three products came from the second factory and (b) none of the three products came from the second factory.

  1.  The probability that all three products came from the second factory is
  2.  The probability that none of the three products came from the second factory is
  1.  The probability that all three products came from the second factory is
    (Round to the nearest thousandth as needed.)
    b.  The probability that none of the three products came from the second factory is
    (Round to the nearest thousandth as needed.)

8  A standard deck of cards contains 52 cards. One card is selected from the deck.

  1.  Compute the probability of randomly selecting a spade or heart
    b.  Compute the probability of randomly selecting a spade or heart or diamond
    c.  Compute the probability of randomly selecting a seven or club
  2.  P(spade of heart)= (Type an integer or a simplified fraction.)
  3.  P(spade or heart or diamond)= (Type an integer or a simplified fraction.)
  4.  P(seven or club)= (Type an integer or a simplified fraction.)

8  A standard deck of cards contains 52 cards. One card is selected from the deck.

  1.  Compute the probability of randomly selecting a three or eight
    b.  Compute the probability of randomly selecting a three or eight of king
    c.  Compute the probability of randomly selecting a queen or diamond
  2.  P(spade of heart)= (Type an integer or a simplified fraction.)
  3.  P(spade or heart or diamond)= (Type an integer or a simplified fraction.)
  4.  P(seven or club)= (Type an integer or a simplified fraction.)

9  The percent distribution of live multiple-delivery births (three or more babies) in a particular year for a women 15 to 54 years old is shown in the pie chart. Find each probability.

10  The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random.  Complete parts (a) through (d).

Nursing majors                        Non-nursing majors                 Total

Males                                       92                                1019                            1111
Females                                   700                              1725                            2425
Total                                        792                              2744                            3536

  1.  Find the probability that the student is male or a nursing major

P (being male or being nursing major) =

  1.  Find the probability that the student is female or not a nursing major.

P( being female or not a nursing major) =

  1.  Find the probability that the student is not female or a nursing major

P(not being female or being a nursing major) =

Are the events “being male” and “being a nursing major” mutually exclusive?

  1.  No, because there are 92 males majoring in nursing
  2.  No, because one can’t be male and a nursing major at the same time
  3.  Yes, because one can’t be male and a nursing major at the same time
  4.  Yes, because there are 97 males majoring in nursing

10  The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random.  Complete parts (a) through (d).

Nursing majors                        Non-nursing majors                 Total

Males                                       97                                1017                            1114
Females                                   700                              1727                            2427
Total                                        797                              2744                            3541

  1.  Find the probability that the student is male or a nursing major

P (being male or being nursing major) =

  1.  Find the probability that the student is female or not a nursing major.

P( being female or not a nursing major) =

  1.  Find the probability that the student is not female or a nursing major

P(not being female or being a nursing major)

Are the events “being male” and “being a nursing major” mutually exclusive?

  1.  No, because there are 97 males majoring in nursing
  2.  No, because one can’t be male and a nursing major at the same time
  3.  Yes, because one can’t be male and a nursing major at the same time
  4.  Yes, because there are 97 males majoring in nursing
  5. Outside a home, there is a 4-key keypad with the letters a,b,c, and d that can open the garage if the correct 4 letter code is entered. Each key may only be used once, how many possible codes are there?

11   Outside a home, there is an 10-key keypad with letters A, B, C, D, E, F, G and H that can be used to open the garage if the correct ten-letter code is entered. Each key may be used only once.  How many codes are possible?

The number of possible codes is

  1. Outside a home, there is a 4-key keypad with the letters a,b,c, and d that can open the garage if the correct 4 letter code is entered. Each key may only be used once, how many possible codes are there?

12  How many different 10-letter words (real or imaginary) can be formed from the following letters?
Z, V, U, G, X, V, H, G, D

ten-letter words (real or imaginary) can be formed with the given letters.

12  How many different 10-letter words (real or imaginary) can be formed from the following letters?
K, I, B, W, E, Z, I, O, R, Z

ten-letter words (real or imaginary) can be formed with the given letters.

  1. A horse race has 13 entries and one person owns 2 of those horses. Assuming that there are no ties, what is the probability that those 2 horses finish first and second (regardless of order)

13  A horse race has 13 entries and one person owns 2 of those horses. Assuming that there are no ties, what is the probability that those four horses finish first, second, third, and fourth (regardless of order)?

The probability that those two horses finish first, second, third, and fourth is

13  A horse race has 13 entries and one person owns 4 of those horses. Assuming that there are no ties, what is the probability that those four horses finish first, second, third, and fourth (regardless of order)?

The probability that those four horses finish first, second, third, and fourth is

  1. Determine the required value of the missing probability to make the distribution a discrete probability distribution.

14  Determine the required value of the missing probability to make the distribution a discrete probability distribution.

X         P(x)
3          0.19
4          ?
5          0.34
6          0.28

P() = (Type an integer or a decimal)

14  Determine the required value of the missing probability to make the distribution a discrete probability distribution.

X         P(x)
3          0.16
4          ?
5          0.38
6          0.17

P() = (Type an integer or a decimal)

  1. A frequency distribution is shown below. Complete a – e.

X         P(x)
0          0.635
1          0.228
2          0.089
3          0.024
4          0.014
5          0.009

15.

Students in a class take a quiz with 8 questions. The number x of questions answered correctly can be approximated by the following probability distribution. Complete a – e.

15  A frequency distribution is shown below. Complete parts (a) through (e).

Dogs                0          1          2          3          4          5
Household       1324    436      162      46        27        15

  1.  Use the frequency distribution to construct a probability distribution.

X         P(x)
0
1
2
3
4
5

  1.  Find the mean of the probability distribution

µ = (Round to the nearest thousandth as needed.)

  1.  Find the variance of the probability distribution

= (Round to the nearest tenth as needed)

  1.  Find the standard deviation of the probability distribution
  • = (Round to the nearest tenth as needed)
  • e.  Interpret the results in the context of the real-life situation.
  • A.  A household on average has 0.5 dog with a standard deviation of 0.9 dog.
  1. B.  A household on average has 0.5 dog with a standard deviation of 15 dog.
  2. C.  A household on average has 0.9 dog with a standard deviation of 0.5 dog.
  3. D.  A household on average has 0.9 dog with a standard deviation of 0.9 dog.

17  Students in a class take a quiz with eight questions. The number x of questions answered correctly can be approximated by the following probability distribution.  Complete parts (a) through (e).

X         0          1          2          3          4          5          6          7          8

P(x)     0.02     0.02     0.06     0.06     0.14     0.24     0.27     0.12     0.07

(a)  Use the probability distribution to find the mean of the probability distribution
µ =
(b)  Use the probability distribution to find the variance of the probability distribution
=
(c)  Use the probability distribution to find the standard deviation of the probability distribution
(d)  Use the probability distribution to find the expected value of the probability distribution

Interpret the results

  1.  The expected number of questions answered correctly is 5.1 with a standard deviation of 1.8 questions.
  2.  The expected number of questions answered correctly is 1.8 with a standard deviation of 5.1 questions.
  3.  The expected number of questions answered correctly is 5.1 with a standard deviation of 0.02 questions.
  4.  The expected number of questions answered correctly is 3.1 with a standard deviation of 1.8 questions.

Statistics for Decision Making

Homework Week 4

https://www.hiqualitytutorials.com/product/math221-homework-week-4/

    1. The histograms each represents part of a binomial distribution. Each distribution has the same probability of success, p, but different numbers of trials, n.  Identify the unusual values of x in each histogram
  1.  Choose the correct answer below. Use histogram
  2.  X = 0, x = 1, x = 2, x = 3, and x = 4
    B.  X = 3 and x = 4
    C.  X = 0 and x = 1
    D.  There are no unusual values of x in the histogram
  3.  X = 7
  4.  X = 0, x = 1, x = 2, x = 3, and x = 4
    B.  X = 0 and x = 1
    C.  X = 0 and x = 1
    D.  There are no unusual values of x in the histogram

2  The histograms each represents part of a binomial distribution. Each distribution has the same probability of success, p, but different numbers of trials, n.  Identify the unusual values of x in each histogram.

(a)  N = 4
(b)  N = 8

  1.  Choose the correct answer below. Use histogram (a).
  2.  X = 4
    B.  X = 0, x =7, and x = 8
    C.  X = 2
    D.  There are no unusual values of x in the histogram
  3.  Choose the correct answer below. Use the histogram (b)
  4.  X =0, x =7, and x = 8
    B.  X = 4
    C.  X = 4
    D.  There are no unusual values of x in the histogram

2  The histograms each represents part of a binomial distribution. Each distribution has the same probability of success, p, but different numbers of trials, n.  Identify the unusual values of x in each histogram.

(a)  N = 4
(b)  N = 8

  1. Choose the correct answer below. Use histogram (a)
  2. X = 4
    B. X = 0, x =7, and x = 8
    C. X = 2
    D. There are no unusual values of x in the histogram

b.Choose the correct answer below. Use the histogram (b)

  1. X =0, x =7, and x = 8
    B. X = 4
    C. X = 4
    D. There are no unusual values of x in the histogram
  2. About 30% of babies born with a certain ailment recover fully. A hospital is caring for 7 babies born with this ailment. The random variable represents the # of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specific the values of n, p , and q, and list the values of random variable x.

3  About 80% of babies born with a certain ailment recover fully. A hospital is caring for five babies born with this ailment.  The random variable represents the number of babies that recover fully.  Decide whether the experiment is a binomial experiment.  If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.

Is the experiment a binomial experiment?

Yes
No

What is a success in this experiment?

Baby doesn’t recover
Baby recovers
This is not a binomial experiment
Specify the value of n.  Select the correct choice below and fill in any answer boxes in your choice.
N =
This is not a binomial experiment
Specify the value of p.  Select the correct choice below and fill in any answer boxes in your choice.
P =
This is not a binomial experiment
Specify the value of q.  Select the correct choice below and fill in any answer boxes in your choice.
Q =
This is not a binomial experiment

List the possible values of the random variable x.

X = 1, 2, 3,…, 5
X = 0, 1, 2, ….4
X = 0, 1, 2, …5

This is not a binomial experiment

3  About 70% of babies born with a certain ailment recover fully. A hospital is caring for six babies born with this ailment.  The random variable represents the number of babies that recover fully.  Decide whether the experiment is a binomial experiment.  If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.

Is the experiment a binomial experiment?

  1.  No
    B.  Yes

What is a success in this experiment?

  1.  Baby recovers
    B.  Baby doesn’t recover
    C.  This is not a binomial experiment

Specify the value of n.  Select the correct choice below and fill in any answer boxes in your choice.

  1.  N =
    B.  This is not a binomial experiment

Specify the value of p. Select the correct choice below and fill in any answer boxes in your choice.
p=

This is not a binomial experiment

Specify the value of q. Select the correct choice below and fill in any answer boxes in your choice.
q =

This is not a binomial experiment

List the possible values of the random variable x.

  1.  X = 0, 1, 2,…,5
    B.  X = 0, 1, 2,…6
    C.  X = 1, 2, 3,…6
    D.  This is not a binomial experiment
    1. Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.
      n = 125, p = 0.81

4  Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.

N = 129, p = 0.43

The mean, µ is (Round to the nearest tenth as needed.)
The variance,  is (Round to the nearest tenth as needed.)

The standard deviation,  is (Round to the nearest tenth as needed.)

    1. 56% of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability that the # who consider themselves baseball fans is (a) 8, (b) at least 8, (c) less than 8.

5  Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.

N = 121, p = 0.27
The mean, µ is (Round to the nearest tenth as needed.)
The variance,  is (Round to the nearest tenth as needed.)
The standard deviation,  is (Round to the nearest tenth as needed.)

    1. 45% of households say they would feel secure if they had at least $50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had $50,000 in savings. Find the probability that the # that they say would feel secure is (a) exactly 5, (b) more than 5 or (c) at most 5.

6  48% of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan.  Find the probability that the number who consider themselves baseball fans is (a) exactly eight, (b) at least eight, and (c) less than eight.  If convenient, use technology to find the probabilities.

  1.  P(8) = (Round to the nearest thousandth as needed)
    b.  P(x≥8) = (Round to the nearest thousandth as needed)
    c.  P(x<8) = (Round to the nearest thousandth as needed)
    1. 43% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask them to name his or her favorite nut. Find the probability that the # who say cashews are their favorite nut is (a) exactly 4, (b) at least 4, and (c) at most 2.

7  Seventy-five percent of households say they would feel secure if they had $50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had $50,000 in savings.  Find the probability that the number that say they would feel secure is (a) exactly five, (b) more than five, and (c) at most five.

  1.  Find the probability that the number that say they would feel secure is exactly five.
    P(5) = (Round to three decimal places as needed)
    b.  Find the probability that the number sat they would feel secure is more than five.
    P(x>5) = (Round to three decimal places as needed)
    c.  Find the probability that the number that say they would feel secure is at most five.
    P(x≤5) = (Round to three decimal places as needed)
    1. 24% of college students say they use credit cards. You randomly select 10 students and ask them why they use credit cards because of the rewards program. (a) Exactly 2, (b) more than 2, and (c) between 2 and 5 inclusive.

8  Sixty-five percent of households say they would feel secure if they had $50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had $50,000 in savings.  Find the probability that the number that say they would feel secure is (a) exactly five, (b) more than five, and (c) at most five.

  1.  Find the probability that the number that say they would feel secure is exactly five.
    P(5) = (Round to three decimal places as needed)
    b.  Find the probability that the number sat they would feel secure is more than five.
    P(x>5) = (Round to three decimal places as needed)
    c.  Find the probability that the number that say they would feel secure is at most five.
    P(x≤5) = (Round to three decimal places as needed)
    1. 34% of women consider themselves of baseball. You randomly select 6 women and ask each if she considers herself a fan of baseball.

X         p(x)
0          0.083
1          0.255
2          0.329
3          0.226
4          0.087
5          0.018
6          0.002

Statistics for Decision Making

9  34% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut.  Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient, use technology to find the probabilities.

  1.  P(3) = (Round to the nearest thousandth as needed.)
    b.  P(x > 4) = (Round to the nearest thousandth as needed.)
    c.  P(x < 2) = (Round to the nearest thousandth as needed)
    1. Given that x has a Poisson distribution with mean = 4, what is the probability that x = 2?

10   33% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut.  Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient, use technology to find the probabilities

  1.  P(3) = (Round to the nearest thousandth as needed.)
    b.  P(x > 4) = (Round to the nearest thousandth as needed.)
    c.  P(x < 2) = (Round to the nearest thousandth as needed)
    1. Given that x has a Poisson distribution with mean = 1.9, what is the probability that x = 3?
  1.  21% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the # of college students who say they use credit cards because of the rewards program is (a) exactly 2, (b) more than 2, and (c) between 2 and 5 inclusive. If convenient, use technology to find the probabilities.
  2.  P(2) = (Round to the nearest thousandth as needed.)
    b.  P(X > 2) = (Round to the nearest thousandth as needed.)
    c.  P(X < 5) = (Round to the nearest thousandth as needed.)
    1. Decide whether binomial, geometric, or Poisson applies to this question.
      In a certain city, the mean # of days with 0.01 inch or more precipitation for May is 13.What is the probability that the city has 21 days with 0.01 inch or more next may?
  1.  38% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the # of college students who say they use credit cards because of the rewards program is (a) exactly 2, (b) more than 2, and (c) between 2 and 5 inclusive. If convenient, use technology to find the probabilities.
  2.  P(2) = (Round to the nearest thousandth as needed.)
    b.  P(X > 2) = (Round to the nearest thousandth as needed.)
    c.  P(X < 5) = (Round to the nearest thousandth as needed.)
    1. Decide whether binomial, geometric, or Poisson applies to this question.
      The mean # of oil tankers at a port city is 6 per day. The port has facilities to handle up to 9 oil tankers in a day. What is the probability that too many tankers will arrive on a given day?
  1.  36% of women consider themselves fan of professional baseball. You randomly select 6 women and ask each if they consider themselves a fan of professional baseball.
  2.  Construct a binomial distribution using n = 6 and p = 0.36

X                     P(x)
0
1

  1.  Choose the correct histogram for this distribution below.
  2.  Describe the shape of the histogram
  3.  Skewed right
    B.  Skewed left
    C.  Symmetrical
    D.  None of these
  4.  Find the mean of the binomial distribution

µ = (round to the nearest 10th as needed)
( e ) find the variance of the binomial distribution.
= (round to the nearest 10th as needed.)
( f ) Find the standard deviation of the binomial distribution.
= (round to the nearest 10th as needed)
( g ) Interpret the results in the context of the real-life situation. What values of the random variable would you consider unusual? Explain your reasoning.

On average, out of 6 women consider themselves baseball fans, with a standard deviation of  women. The values x=6 and x= would be unusual because their probabilities are less than 0.05.

    1. Find the indicated probabilities using geometric distribution or Poisson distribution. Then determine if the events are unusual. If convenient, use a Poisson probability table or technology to find the probabilities.

Assume the probability that you will make a sale on any given telephone call is 0.18. find the probability that you (a) make your first sale on the 5th call, (b) make your sale on the 1st, 2nd, or 3rd call, and (C) do not make the sale on the first 3 calls.

  1.  38% of women consider themselves fan of professional baseball. You randomly select 6 women and ask each if they consider themselves a fan of professional baseball

(a) Construct a binomial distribution using n = 6 and p = 0.38

X                     P(x
0
1
2
3
4
5
6

(b)  Choose the correct histogram for this distribution below.

(c).  Describe the shape of the histogram

  1.  Skewed right
    B.  Skewed left
    C.  Symmetrical
    D.  None of these

(d)  Find the mean of the binomial distribution
µ = (round to the nearest 10th as needed)
( e ) find the variance of the binomial distribution.
= (round to the nearest 10th as needed.)
( f ) Find the standard deviation of the binomial distribution.
=  (round to the nearest 10th as needed)
( g ) Interpret the results in the context of the real-life situation. What values of the random variable would you consider unusual? Explain your reasoning.

On average, out of 6 women consider themselves baseball fans, with a standard deviation of women. The values x= and x= would be unusual because their probabilities are less than .

    1. Find the indicated probabilities using geometric distribution or Poisson distribution. Then determine if the events are unusual. If convenient, use a Poisson probability table or technology to find the probabilities. A newspaper finds that the mean # of typographical errors per page is 7. Find the probability that (a) exactly 6 typos are found on a page, (b) at most 6 are found on a page, and (c) more than 6 are found on a page.
    2. Find the indicated probabilities using geometric distribution or Poisson distribution. Then determine if the events are unusual. If convenient, use a Poisson probability table or technology to find the probabilities. A major hurricane is a hurricane with wind speeds of 111 miles per hour or more. During the last century, the mean # of major hurricanes to strike was about 0.62. find the probability that in a given year is (a) exactly one hurricane, (b) at most one, and (c) more than one.
  1.  Given that x has a Poisson distribution with µ = 3, what is the probability that x = 5?

P(5) ≈ (round to 4 decimal places as needed.)

    1. Given that x has a Poisson distribution with µ = 4, what is the probability that x = 3?

P(3) ≈ (round to 4 decimal places as needed.)

    1. Given that x has a Poisson distribution with µ = 1.6, what is the probability that x = 5?

P(5) ≈ (round to 4 decimal places as needed.)

    1. Given that x has a Poisson distribution with µ = 0.5, what is the probability that x = 0?

P(0) ≈ (round to 4 decimal places as needed.)

    1. Decide which probability distribution – binomial, geometric, or Poisson – applies to the question. You do not need 2 answer the question.

Given: of students ages 16 to 18 with A or B averages who plan to attend college after graduation, 60% cheated to get higher grades. 10 randomly chosen students with A or B to attend college after graduation were asked if they cheated to get higher grades. Question: what is the probability that exactly two students answered no?

  1.  Poisson distribution
    B.  Binomial distribution
    C.  Geometric distribution
    1. Decide which probability distribution – binomial, geometric, or Poisson – applies to the question. You do not need 2 answer the question. Instead, justify your choice.
      Question: what is the probability that t00 many tankers will arrive on a given day?
  1. Binomial.  You are interested in counting the number of successes out of n trials.
    B. Poisson.  You are interested in counting the number of occurrences that take place within a given unit of time.
    C.  Geometric.  You are interested in counting the number of trials until the first success.
    1. Decide which probability distribution – binomial, geometric, or Poisson – applies to the question. You do not need to answer the question.

Given: Of students ages 16 to 18 with A or B averages who plan to attend college after graduation, 65% cheated to get higher grades.  Ten randomly chosen students with A or B attend college after graduation were asked if the cheated to get higher grades.  Question: What is the probability that exactly two students answered no?

What type of distribution applies to the given question?

  1.  Binomial distribution
    B,  Geometric distribution
    C.  Poisson distribution
    1. Decide which probability distribution – binomial, geometric, or Poisson – applies to the question. You do not need to answer the question.  Instead, justify your choice.

Given: The mean number of oil tankers at a port city is 12 per day.  The port has facilities to handle up to 18 oil tankers in a day.

Choose the correct probability distribution below.

  1.  Poisson.  You are interested in counting the number of occurrences that take place within a given unit of time.
    B.  Binomial.  You are interested in counting the number of successes out of n trials.
    C.  Geometric.  You are interested in counting the number of trials until the first success.
    1. Find the indicated probabilities using the geometric distribution or Poisson distribution. Then determine if the events are unusual. If convenient, use a Poisson probability table or technology to find the probabilities.

Assume the probability that you will make a sale on any given telephone call is 0.14. Find the probability that you (a) make your first sale on the fifth call, (b) make your sale on the 1st, 2nd, or 3rd call, and (c) do not make a sale on the first 3 calls.
(a) P(make your first sale on the fifth call) =
(Round to three decimal places as needed.)
(b) P(make your sale on the first, second, or third call) =
(Round to three decimal places as needed.)
(c) P(do not make a sale on the first three calls) =
(Round to three decimal places as needed.)

Which of the events are unusual?  Select all that apply.

  1.  The event in part (a), “make your first sale on the fifth call”, is unusual
    B. The event in part (b), “make you sale on the first, second, or third call”, is unusualC.
    C.  The event in part (c), “do not make a sale on the first three calls”, is unusual
    D.  None of the events are unusual
    1. Find the indicted probabilities using the geometric distribution or Poisson distribution. Then determine if the events are unusual. If convenient, use a Poisson probability table or technology to find the probabilities.
      A newspaper finds the mean number of typographical errors per page is four. Find the probability that (a) exactly five typographical errors are found on a page, (b) at most five typographical errors are found on a page, and (c) more than five typo errors are found on a page.
      (a) P(exactly five typo errors are found on a page) =
      (Round to four decimal places as needed.)
    2. (b)P(at most five typographical errors are found on a page) =

(Round to four decimal places as needed.)
(c) P(more than five typo errors are found on a page) =
(Round to four decimal places as needed)

Which of the events are unusual?  Select all that apply.

  1.  The event in part (a) is unusual.
    B.  The event in part (b) is unusual.
    C.  The event in part (c) is unusual.
    D.  None of the events are unusual
    1. Find the indicted probabilities using the geometric distribution or Poisson distribution. Then determine if the events are unusual. If convenient, use a Poisson probability table or technology to find the probabilities.

A major hurricane is a hurricane with winds of 111 mph or greater. During the lsat century, the mean # of major hurricanes to strike a certain country’s mainland per year was about 0.46. Find the probability that in a given year (a) exactly one major hurricane will strike the mainland, (b) at most one major hurricane will strike the mainland, and (c) more than one major hurricane will strike the mainland.
(a) P(exactly one major hurricane will strike the mainland) =
(Round to three decimal places as needed.)
(b) P(at most one major hurricane will strike the mainland) =
(Round to three decimal places as needed.)
(c) P(more than one major hurricane will strike the mainland) =
(Round to three decimal places as needed.)

Which of the events are unusual?  Select all that apply.

  1.  The event in part (a) is unusual.
    B.  The event in part (b) is unusual.
    C.  The event in part (c) is unusual.
    D.  None of the events are unusual

Statistics for Decision Making

Homework Week 5

https://www.hiqualitytutorials.com/product/math221-homework-week-5/

1 A study was conducted that resulted in the following relative frequency histogram. Determine whether or not the histogram indicates a normal distribution could be used a model for the variable.

  1.  The histogram is not bell-shaped, so a normal distribution could not be used as a model for the variable.
    B.  The histogram is bell-shaped, so a normal distribution could be used as a model for the variable.
    C.  The histogram is not bell-shaped, so a normal distribution could be used as a model for the variable.
    D.  The histogram is bell-shaped, so a normal distribution could not be used as a model for the variable.

1  A study was conducted that resulted in the following relative frequency histogram. Determine whether or not the histogram indicates a normal distribution could be used a model for the variable.

1.

A study was conducted that resulted in the following relative frequency histogram. Determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.

  1.  The histogram is not bell-shaped, so a normal distribution could not be used as a model for the variable.
    B.  The histogram is bell-shaped, so a normal distribution could be used as a model for the variable.
    C.  The histogram is not bell-shaped, so a normal distribution could be used as a model for the variable.
    D.  The histogram is bell-shaped, so a normal distribution could not be used as a model for the variable.

2 Find the area of the shaded region. The graph depicts  the standard normal distribution with mean 0 and standard deviation 1.

The area of the shaded region is
(round to 4 decimal places as needed.)

2.

Find the area of the shaded region.

F  Find the area of the indicated region under the standard normal curve

The area between z = 0 and z = 1 under the standard normal curve is
(round to 4 decimal places as needed.)

3  Find the area of the indicated region under the standard normal curve.

The area between z  = 0 and z = 1.3 under the standard normal curve is
(round to 4 decimal places as needed.)

4  Find the indicated area under the standard normal curve.
To the left of z =

The area to the left of z = -0.28 under the standard normal curve is
(round to 4 decimal places as needed.)
4  Find the indicated area under the standard normal curve.
To the left of z =
The area to the left of z = – 0.28 under the standard normal curve is
round to four decimal places as needed.

  1. Find the area under the standard normal curve. To the left of z = 2.26

5 Find the indicated area under the normal curve.
between z = -1.08 and z = 1.08
The area between z= -1.08 and z = 1.08 under the standard normal curve is
(round to 4 decimal places as needed.)

  1. Find the indicated area under the standard normal curve. To the right of z = 0.42

6  Find the indicated area under the standard normal curve.
To the left of z =

The area to the left of z = under the standard curve is

6  Find the indicated area under the standard normal curve.

To the right of z =

The area to the right of z = under the standard normal curve is.

6  Find the indicated area under the standard normal curve.

Between z = and z =

The area between z = and z = under the standard normal curve is.

  1. Find the indicated area under the standard normal curve. Between z = -0.48 and 0.48

7  Assume the random variable x is normally distributed with mean µ = 82 and standard deviation .  Find the indicated probability.

P(x<75)

P(x<75) = (Round to four decimal places as needed)

7  Assume random variable x is normally distributed with mean µ = 82 and standard deviation. Find the indicated probability.

P(x<78)
P(X<78) = (round to 4 decimal places as needed.

7  Assume random variable x is normally distributed with mean µ = 87 and standard deviation . Find the indicated probability.
P(75<x<84)
P(75<x<84) =
(round to 4 decimal places as needed.)

  1. Assume the random variable x is normally distributed with a mean of 81 and standard deviation of 4. P(X<77)

8 Assume the random variable x is normally distributed with mean µ = 84 and standard deviation σ = 5.  Find the indicated probability.

P(68<x<74)
P(68<x74<) =

(Round to four decimal places as needed)

  1. Assume the random variable x is distributed with mean of 90 and standard deviation of 5. P(63<x<88)

9  A survey was conducted to measure the height of men.  In the survey, respondents were grouped by age.  In the 20-29 age group, the heights were normally distributed, with a mean of 67.5 inches and a standard deviation of 2.0 inches.  A study participant is randomly selected.  Complete parts (a) through (c).

  1.  Find the probability that his height is less than 67 inches.
    The probability that the study participant selected at random is less than 67 inches tall is (Round to four decimal places as needed)
    b.  Find the probability that his height is between 67 and 72 inches.
    The probability that the study participant selected at random is between 67 inches and 72 inches tall is. (Round to four decimal places as needed)
    c.  Find the probability that his height is more than 72 inches.
    The probability that the study participant selected at random is more than 72 inches tall is (Round to four decimal places as needed)

9  A survey was conducted to measure the height of men. In the survey, respondents were grouped by age. In the 20-29 group, the heights were normally distributed, with a mean of 69.9 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts (a) through (c).

  1. find the probability that his height is less than 68 inches.
    The probability that the student participant selected at random is less than 68 inches tall is (round to 4 decimal places as needed.)
    B. find the probability that his height is between 68 and 71 inches
    the probability that the student participant selected at random is between 68 and 71 inches tall is   (round to 4 decimal places as needed.)
  2.  find the probability that his height is more than 71 inches.

The probability that the study participant selected at random is more than 71 inches tall is (round to 4 decimal places as needed).

  1. A survey was conducted to measure the height of men. In the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with a mean of 69.6 inches and a standard deviation of 3 inches. Complete parts a – c.
    A) Find that probability that his height is less than 65 inches.
    B) Find the probability that his height is between 65-70 inches.
    C Find the probability that his height is more than 70 inches.

10 Use the normal distribution of SAT critical reading scores for which the mean is 515 and the standard deviation is 108.  Assume the variable x is normally distributed.
(a)  What percent of the SAT verbal scores are less than 650?
(b)  If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 575?

  1.  Approximately % of the SAT verbal scores are less than 650. (Round to two decimal places as need)
    b.  You would expect that approximately SAT verbal scores would be greater than 575.  (Round to the nearest whole number as needed)

10 Use the normal distribution of Sat critical reading scores for which the mean is 514 and the standard deviation is 124. Assume the variable x is normally distributed.

  1. Use the normal distribution of SAT crtical reading scores for which the mean is 502 and standard deviation is 119. Assume the variable x is normally distributed.
    A) what % of the SAT scores are less than 675?
    B) if 1000 SAT verbal scores are randomly selected, how many would be greater than 525?
  1. what percent of the SAT verbal score is less than 500?
    B. if 1000 sat scores are randomly selected, how many would be greater than 525?
    A: %
    B: greater than 525

11  Find the indicated z-score shown in the graph to the right.

The z-score is (Round to two decimal places as needed)

11 Find the indicated z-score shown in the graph to the right.

The z-score is

11  Find the indicated z-score shown in the graph to the right.

  1. Find the z-score shown in the graph.

12 Find the indicated z-score shown in the graph to the right.

The z-score is
The z-score is (Round to two decimal places as needed)

  1. Find the z-score shown in the graph.

13  Find the z-score that has 11.9% of the distribution’s area to its right.

The z-score is (Round to two decimal places as needed)

  1. Find the z-score that has 27.1% of the distribution’s area to it’s right

13  Find the z-score that has 11.9% of the distribution’s area to its right.
The z-score is (Round to two decimal places as needed)

14  Find the z-scores for which 70% of the distribution’s area lies between –z and z.
The z-scores are

(Use a comma to separate answers as needed.  Round to two decimal places as needed)

14  Find the z-scores for which 98% of the distribution’s area lies between – z and z.
The z-scores are (Use a comma to separate answers as needed)

  1. Find the z-score for which 70% of the distribution’s area is between –z and z.
  2. In a survey of women in a certain country (ages 20-29), the mean height was 64.9 inches with a standard deviation of 2.86 inches. Answer the following questions:
    A) what height represents the 85th percentile
    B) what height represents the first quartile?

15 In a survey of women in a certain country (ages 20-29), the mean height was 66.5 inches with a standard deviation of 2.84 inches.  Answer the following questions about the specified normal distribution.

(a)  What height represents the 85th percentile?
(b)  What height represents the first quartile?

  1.  The height the represents the 85th percentile is inches. (Round to two decimal places as needed)
    b.  The height that represents the first quartile is inches. (Round to two decimal places as needed)

15  In a survey of women in a certain country (ages 20-29), the mean height was 65.9 inches with a standard deviation of 2.74 inches. Answer the following questions about the specified normal distribution.

(a)  What height represents the 95th percentile?
(b)  What height represents the first quartile?

  1.  The height that represents the 95th percentile is inches. (Round to two decimal places as needed)
    b.  The height that represents the first quartile is inches. (Round to two decimal places as needed)

16  The time spent (in days) waiting for a heart transplant in two states for patients with type A + blood can be approximately by a normal distribution, as shown in the graph.  Complete parts (a) and (b) below.

(a)  What is the shortest time spent waiting for a heart that would still place a patient in the top 30% of waiting times?
days (Round to two decimal places as needed)
(b) What is the longest time spent waiting for a heart that would still place a patient in the bottom 29% of waiting times?

days. (Round to two decimal places as needed)

16  The time spent (in days) waiting for a heart transplant in two states for patients with type A + blood can be approximated by a normal distribution, as shown in the graph to the right. Complete parts (a) and (b) below.

(a)  What is the shortest time spent waiting for a heart that would still place a patient in the top 15% or waiting times?
days ( Round to two decimal places as needed)
(b) What is the longest time spent waiting for a heart that would still place a patient in the bottom 5% of waiting times?
days ( Round to two decimal places as needed)

  1. The time spent waiting for a heart transplant in two states for patients with type A blood can be approximated by a normal distribution, as shown in the graph to the right.
    A) what is the shortest time spent waiting for a heart that would still place a patient in the top 30% of waiting times?
    B) what is the longest time spent waiting for a heart that would still place a patient in the bottom 1% of waiting times?

17   population has a mean µ = 86 and a standard deviation σ = 14.  Find the mean and standard deviation of a sampling distribution of a sampling distribution of sample means with sample size n = 49.

  1. A population has a mean of 90 and standard deviation of 12. Find the mean and standard deviation of a sampling distribution of sample means with sample size n =36

Statistics for Decision Making

18  The graph of the waiting time (in seconds) at a red light is shown below on the left with its mean and standard deviation. Assume that a sample size of 100 is drawn from the population.  Decide which of the graphs labeled (a)-(c) would most closely resemble the sampling distribution of the sample means.  Explain your reasoning.

  1. The graph of waiting times at a red light is shown below on the left with its mean and standard deviation. Assume that a sample size of 100 is drawn from the population. Decide which of the graphs labeled a – c would most likely resemble the sampling distribution of the sample means.

18  The graph of the waiting time (in seconds) at a red light is shown below on the left with its mean and standard deviation.  Assume that a sample size of 100 is drawn from the population.  Decide which of the graphs labeled (a)-(c) would most closely resemble the sampling distribution of the sample means.  Explain your reasoning.

Graph ( ) most closely resembles the sampling distribution of the sample means, because

µ – =, σ – =, and the graph approximates a normal curve.

X              x

(Type an integer or a decimal)

19 A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 133 ounces and a standard deviation of 0.30 ounce.  You randomly select 50 cans and carefully measure the contents.  The sample mean of the cans is 132.9 ounces.  Does the machine need to be reset?  Explain your reasoning.

19  A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 132 ounces and a standard deviation of 0.30 ounces. You randomly select 45 cans and carefully measure the contents. The sample mean of the cans is 131.9 ounces.  Does the machine need to be reset?  Explain your reasoning.

20  A manufacturer claim that the life span of its tires is 50,000 miles.  You work for a consumer protection agency and you are testing these tires.  Assume the life spans of the tires are normally distributed.  You select 100 tires at random and test them.  The mean life span is 49,741 miles.  Assume σ = 900.  Complete parts (a) through (c)

  1.  Assuming the manufacturer’s claim is correct, what is the probability that the mean of the sample is 49,741 miles of less?
    (Round to four decimal places as needed)
    b.  using your answer form part (a), what do you think of the manufacturer’s claim?
    c.  ssuming the manufacturer’s claim is true, would it be unusual to have an individual tire with a life span of 49, 741 mile? Why or why not?
  1. A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispenses has a mean of 122 ounces and a standard deviation of 0.30 ounce. You randomly select 40 cans and carefully measure the contents. The sample mean of cans is 121.9 ounces. Does the machine need to be reset? Explain your reasoning.

20  A manufacturer claims that the life span of its tires is 49,000 miles. You work for a consumer protection agency and you are testing these tires. Assume the life spans of the tires are normally distributed.  You select 100 tires at random and test them.  The mean life span is 48, 778 miles.  Assume σ = 900. Complete parts (a) through (c).

  1.  Assuming the manufacturer’s claim is correct, what is the probability that the mean of the sample is 48,778 miles or less?
    (Round to four decimal places as needed)
    b.  Using your answer from part (a), what do you think of the manufacturer’s claim?.
    c.  Assuming the manufacturer’s claim is true, would it be unusual to have an individual tire with a life span of 48,778 mile? Why or why not?
  2. A manufacturer claims that the life spam of its tires is 49,000 miles. You work for a consumer protection agency and you are testing these tires. Assume the life spans of the tires are normally distributed. You select 100 tires at random and test them. The mean life span is 48,807 miles. Assume the mean = 800.

Statistics for Decision Making

Homework Week 6

https://www.hiqualitytutorials.com/product/math221-homework-week-6/

1  Given the same sample statistics, which level of confidence would produce the widest confidence interval?

Choose the correct answer below.

  1.  90%
    B.  98
    C.  99%
    D.  95%
  1. Given the same sample statistics, which level of confidence would produce the widest confidence interval?

Choose the correct answer below.

  1.  99%
    B.  95%
    C.  98%
    D.  90%

Use the values on the number line to find the sampling error.

The sampling error is

  1. Use the following values to find the sampling error:
    u = 25.36
    x = 26.74

3  Find the margin of error for the given values of c, s, and n.
C=0.90, s=3.4, n=81
E= (Round to three decimal places as needed)

3  Find the margin of error for the given values of c, s, and n.
C=0.90, s=3.6, n=81

  1. Find the margin of error for the given values of c,s, and n.
    C = 0.95, S = 3.1, N = 64

E= (Round to three decimal places as needed)

4  Construct the confidence interval for the population mean µ.

A 98% confidence interval for µ is ( ) (Round to two decimal places as needed)

4  Construct the confidence interval for the population meanµ.

  1. Construct the confidence interval for the population mean.
    c = 0.90, x = 5.9, s = 0.8, and n = 44

A 98% confidence interval for µ is ( ),  (Round to two decimal places as needed)

5  Construct the confidence interval for the population mean µ.

A 90% confidence interval for µ is ( ). (Round to one decimal place as needed)

5  Construct the confidence interval for the population mean µ.

  1. Construct the confidence interval for the population mean.
    c = 0.90, x = 15.7, s = 10.0, and n = 80

A 98% confidence interval for µ is ( ). (Round to one decimal place as needed)

6  Use the confidence interval to find the estimated margin of error.  Then find the sample mean.
A biologist reports a confidence interval of (4.3,5.1) when estimating the mean height (in centimeters) of a sample of seedlings.

The estimated margin of error is
The sample mean is

6  Use the confidence interval to find the estimated margin of error. Then find the sample mean.
A biologist reports a confidence interval of (1.6,3.2) when estimating the mean height (in centimeters) of a sample of seedlings.

The estimated margin of error is
The sample mean is

  1. Use the confidence interval to find the estimated margin of terror. Then find the mean.
    A biologist reports a confidence interval of (4.7,5.1) when estimating the mean height of a sample of seedlings.

7  Find the minimum sample size n needed to estimate µ for the given values of c, s, and E
C=0.90, s=7.7, and E=1
Assume that a preliminary sample has at least 30 members
N= (Round up to the nearest whole number)
7  Find the minimum sample size n needed to estimate µ for the given values of c, s, and E.
C=0.95, s= 9.3, and E=1
Assume that a preliminary sample has at least 30 members
N= (Round up to the nearest whole number)

7.Find the minimum sample size needed to estimate u for the given values of c, s, and E.
C = 0.90, S = 9.5, E = 1

8.You are given the sample mean and sample standard deviation. Use this information to construct 90% and 95% confidence intervals for the population mean. A random sample of 40 home theater systems has a mean price of $118.00 and standard deviation is $19.50

8  You are given the sample mean and the sample standard deviation.  Use this information to construct the 90% and 95% confidence intervals for the population mean.  Interpret the results and compare the widths of the confidence intervals.  If convenient, use technology to construct the confidence intervals.

A random sample of 55 home theater system has a mean price of $135.00 and a standard deviation is $15.70.
Construct a 90% confidence interval for the population mean.
The 90% confidence interval is ( ) (Round to two decimal places as needed)
Construct a 95% confidence interval for the population mean.
The 95% confidence interval is ( ) (Round to two decimal places as needed)
Interpret the results. Choose the correct answer below.

  1.  With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is wider than 90%.
    B. With 90% confidence, it can be said that the sample mean price lies in the first interval. With 95% confidence, it can be said that the sample mean price lies in the second interval. The 95% confidence interval is wider than the 90%.
    C. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95%, confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is narrower than 90%.

8  You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean.  Interpret the results and compare the widths of the confidence intervals.  If convenient, use technology to construct the confidence intervals.

A random sample of 60 home theater system has a mean price of $115.00 and a standard deviation is $15.10.
Construct a 90% confidence interval for the population mean.
The 90% confidence interval is () (Round to two decimal places as needed)
Construct a 95% confidence interval for the population mean.
The 95% confidence interval is () (Round to two decimal places as needed)

Interpret the results. Choose the correct answer below.

  1. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is wider than 90%.
    B. With 90% confidence, it can be said that the sample mean price lies in the first interval. With 95% confidence, it can be said that the sample mean price lies in the second interval. The 95% confidence interval is wider than the 90%.
    C. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95%, confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is narrower than 90%.

Statistics for Decision Making

9  You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals.
A random sample of 31 gas grills has a mean price of $642.90 and a standard deviation of $58.40.

The 90% confidence interval is ( ) (round to one decimal place as needed)
The 95% confidence interval is ( ) (round to one decimal place as needed)

Which interval is wider?  Choose the correct answer below.

  1.  The 90% confidence interval
    B.  The 95% confidence interval

9.You are given the sample mean and sample standard deviation. Use this information to construct 90% and 95% confidence intervals for the population mean.
A random sample of 46 gas grills has a mean price of $639.50 and standard deviation of $55.40

10  You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals.

A random sample of 33 eight-ounce servings of different juice drinks has a mean of 93.5 calories and a standard deviation of 41.5 calories.
The 90% confidence interval is ( ). (Round to 1 decimal place as needed.)

The 95% confidence interval is ( ). (Round to 1 decimal place as needed.)
Which interval is wider?

  1.  The 95% confidence interval
    B.  The 90% confidence interval

10.You are given the sample mean and sample standard deviation. Use this information to construct 90% and 95% confidence intervals for the population mean.
A random sample of 49 eight ounce servings of different drinks has a mean of 91.9 and standard deviation of 40.3

11  People were polled on how many books they read the previous year. How many subjects are needed to estimate the number of books read the previous year within one book with 90% confidence? Initial survey results indicate that σ=11.7 books

A 90% confidence level requires subjects.

(Round up to the nearest whole number as needed)

11.People were polled on how many books they read the previous year. How many subjects are needed to estimate the # of books read the previous year within 1 book with 95% confidence. O = 15.5 books

12  A doctor wants to estimate the HDL cholesterol of all 20-to 29-year-old females. How many subjects are needed to estimate the HDL cholesterol within 2 points with 99% confidence assuming σ=15.4? Suppose that the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size required?

A % confidence level requires subjects.
(Round up to the nearest whole number as needed)

A % confidence level requires subjects.

(Round up to the nearest whole number as needed)

How does the decrease in confidence affect the sample size required?

  1.  The sample size is the same for all levels of confidence
    B.  The lower the confidence level the larger the sample size
    C.  The lower the confidence level the smaller the sample size

12.A doctor wants to estimate the HDL cholesterol of all 20-29 year olds females. How many subjects are needed to estimate the HDL within 2 points with 99% confidence assuming o = 14.3? Also find out 95% confidence.

13  Construct the indicated confidence interval for the population mean µ using (a) a t-distribution. (b) if you had incorrectly used a normal distribution, which interval would be wider?

(a) The 95% confidence interval using a t-distribution is ( )
(round to one decimal place as needed.)

(b) If you had incorrectly used a normal distribution, which interval would be wider?

  1.  The t-distribution has the wider interval
    B.  The normal distribution has the wider interval

14  In the following situation, assume the random variable is normally distributed and use a normal distribution or a t-distribution to construct a 90% confidence interval for population mean. If convenient, use technology to construct the confidence interval.
(a) In a random sample of 10 adults from a nearby county, the mean waste generated per person per day was 4.65 pounds and the standard deviation was 1.48 pounds.
Repeat part (a), assuming the same statistics came from a sample size of 450. Compare the results.

(a) For the sample size of 10 adults, the 90% confidence interval is ( )
(Round to 2 decimal places as needed.)
(b) For the sample of 450 adults, the 90% confidence interval is ( )
(Round to 2 decimal places as needed.)

Choose the correct observation below

  1. The interval from part (a), which uses the normal distribution, is narrower than the interval from part (b), which uses the t-distribution.
    B. The interval from part (a), which uses the t-distribution, is wider than the interval from part (b), which uses the normal distribution.
    C.  The interval from part (a), which uses the normal distribution, is wider than the interval from part (b), which uses the t-distribution.
    D.  The interval from part (a), which uses the t-distribution, is narrower than the interval from part (b), which uses the normal distribution.

14.In a random sample of 10 adults from a nearby county, the mean waste generated per person per day was 4.58 pounds and standard deviation was 1.04 pounds. Repeat part A and assume the sample size is 450.

15  Use the given confidence interval to find the margin of error and the sample proportion.

(0.662,0.690)
E = (type an integer or a decimal.)

15.Use the given confidence interval to find the margin of error and the sample proportion.
(0.685, 0.713)

  1. In a survey of 654 males aged 18-64, 399 say they have gone to a dentist in the last year. Construct a 90 and 95% confidence interval.

16  In a survey of 633 males from 18-64, 390 say they have gone to the dentist in the past year.
Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.

The 90% confidence interval for the population proportion p is ( )
(Round to 3 decimal places as needed.)
The 95% confidence interval for the population proportion p is ( )
(Round to 3 decimal places as needed.)

Interpret your results of both confidence intervals.

  1.  With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.
    B.  With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is not between the endpoints of the given confidence interval.
    C.  With the given confidence, it can be said that the sample proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.

Which interval is wider?

  1.  The 90% confidence interval
    B,  The 95% confidence interval

17  In a survey of 6000 women, 3431 say they change their nail polish once a week. Construct a 99% confidence interval for the population proportion of women who change their nail polish once a week.
A 99% confidence interval for the population proportion is ( )
(Round to 3 decimal places as needed)

17.In a survey of 9000 women, 6431 say they change their nail polish once a week. Construct a 99% confidence.

  1. a researcher wants to estimate with 99% confidence the # of adults who have high speed internet access. Her estimate must be accurate within 5% of the true proportion.
    A) find the minimum sample size needed, using a prior study that found 46% of the respondents said they have high-speed internet access.
    B) no preliminary estimate is available. Find the minimum sample size needed.

18  A researcher wishes to estimate, with 99% confidence, the proportion of adults who have high-speedy internet access. Her estimate must be accurate within 4% of the true proportion.

  1. a) Find the minimum sample size needed, using a prior study that found that 42% of the respondents said they have a high-speedy internet access.
    b) No preliminary estimate is available. Find the minimum sample size needed.
  2. A) What is the minimum sample size needed using a prior study that found that 42% of the respondents said they have high-speed internet access?
    n = (Round up to the nearest whole # as needed.)
    B) What is the minimum sample size needed assuming that no preliminary estimate is available?
    n = (Round up to the nearest whole # as needed.)

Statistics for Decision Making

Homework Week 7

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    1. Use the given statement to represent a claim. Write it’s complement and state which is Ho and which is Ha.u > 635Find the complement of the claim.
      u < 6351 Use the given statement to represent a claim. Write it’s complement and state which is Ho and which is Ha.u > 635Find the complement of the claim.
      u < 635
    2. A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right tailed, or two-tailed.
    3. What type of test is being conducted in this problem?
    1. A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right tailed, or two-tailed.

What type of test is being conducted in this problem?

    1. Write the null and alternative hypotheses. Identify which is the claim.
      A light bulb manufacturer claims that the mean life of a certain type of light bulb is more than 700 hours.

Identify which is the claim.

3 Write the null and alternative hypotheses. Identify which is the claim.
A light bulb manufacturer claims that the mean life of a certain type of light bulb is more than 700 hours.  Identify which is the claim.

4 Write the null and alternative hypotheses. Identify which is the claim. The standard deviation of the base price of a certain type of car is at least $1010. Identify which is the claim.

    1. Write the null and alternative hypotheses. Identify which is the claim. The standard deviation of the base price of a certain type of car is at least $1010.Identify which is the claim.
    1. More than 11% of all homeowners have a home security alarm. Determine whether the hypothesis for this claim is left-tailed, right-tailed, or two-tailed. Explain your reasoning.
    2. A film developer claims that the mean number of pictures developed for a camera with 22 exposures is less than 17. If a hypothesis test is performed, how should interpret a decision that (a) rejects the null hypothesis and (B) fails to reject the null hypothesis?

A = There is enough evidence to support the claim that the mean number of pictures developed for a camera with 22 exposures is less than 17.
B = There is not enough evidence to support the claim that the mean number of pictures developed for a camera with 22 exposures is less than 17.

6 A film developer claims that the mean number of pictures developed for a camera with 24 exposures is less than 23. If a hypothesis test is performed, how should interpret a decision that (a) rejects the null hypothesis and (B) fails to reject the null hypothesis?

7 Find the P-value for the indicated hypothesis test with the given test statistic, z. Decide whether to reject Ho for the given level of significance a.
Two-tailed test with test statistic z = -2.08 and a = 0.04
P-Value =
Conclusion =

    1. Find the P-value for the indicated hypothesis test with the given test statistic, z. Decide whether to reject Ho for the given level of significance a.
      Two-tailed test with test statistic z = -2.08 and a = 0.04
      P-Value =
      Conclusion =
    2. Find the critical z values. Assume that the normal distribution applies.
      Right-tailed test, a =
      Z =8 Find the critical z values. Assume that the normal distribution applies.
      Right-tailed test, a =
      Z =
    3. Find the critical value(s) for a left-tailed z-test with a = 0.01. Include a graph with your answer.
      Critical Value =

Graph:

9  Find the critical value(s) for a left-tailed z-test with a = 0.01. Include a graph with your answer.
Critical Value = -2.33

Graph:

    1. Test the claim about the population mean, u, at the given level of significance using the given sample statistics.
      Claim u =, a =, sample statistics: x =, s =, n =

Standardized test statistic =
Critical Values =

Statistics for Decision Making

10 Test the claim about the population mean, u, at the given level of significance using the given sample statistics.
Claim u = 50, a = 0.08, sample statistics: x = 49.2, s = 3.56, n = 80

    1. Test the claim about the population mean, u, at the given level of significance using the given sample statistics.
      Claim u = 5000, a = 0.05. Sample statistics x = 4800, s = 323, n = 46.Standardized test statistic =
      Critical Values =
    2. Test the claim about the population mean, u, at the given level of significance using the given sample statistics.
      Claim u = 5000, a = 0.05. Sample statistics x = 4800, s = 323, n = 46.Standardized test statistic =
      Critical Values =
      12 A random sample of 85 eight grade students’ score on a national mathematics assessment test has a mean score of 275 with a standard deviation of 33. This test result prompts a state school administrator to declare that the mean score for the state’s eighth graders on this exam is more than 270. At a = 0.03, is there enough evidence to support the administrators claim? Compare parts A – E.
    3. A random sample of 85 eight grade students’ score on a national mathematics assessment test has a mean score of 275 with a standard deviation of 33. This test result prompts a state school administrator to declare that the mean score for the state’s eighth graders on this exam is more than 270. At a = 0.03, is there enough evidence to support the administrators claim? Compare parts A – E.

Z =
Area =
P Value =

    1. A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 45 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of the cola has a mean caffeine content of 45.5 milligrams with a standard deviation of 6.1 milligrams. At a = 0.08, can you reject the company’s claim?

The critical values are =

z =

    1. A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 975 hours. A random sample of 72 light bulbs has a mean life of 954 hours with a standard deviation of 85 hours. Do you have enough evidence to reject the manufacturer’s claim? Use a = 0.04.

Zo =
Z =

    1. An environmentalist estimates that the mean waste recycled by adults in the country is more than 1 pound per person per day. You want to this test claim. You find that the mean waste recycled per person per day for a random sample of 12 adults in the country is 1.4 pounds and the standard deviation is 0.3 pound. At a = 0.10, can you support the claim? Assume the population is normally distributed.

To =

T =

15 An environmentalist estimates that the mean waste recycled by adults in the country is more than 1 pound per person per day. You want to this test claim. You find that the mean waste recycled per person per day for a random sample of 12 adults in the country is 1.4 pounds and the standard deviation is 0.3 pound. At a = 0.10, can you support the claim? Assume the population is normally distributed.

16 A county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 40 miles per hour. A random sample of 25 vehicles has a mean speed of 45 miles per hour and a standard deviation of 5.4 miles per hour. At a = 0.10, do you have enough evidence to support the county’s claim? Complete parts A – D.

    1. A county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 40 miles per hour. A random sample of 25 vehicles has a mean speed of 45 miles per hour and a standard deviation of 5.4 miles per hour. At a = 0.10, do you have enough evidence to support the county’s claim? Complete parts A through D.T =
      P- Value =
    2. A traveled association claims that the mean daily meal cost for two adults traveling together on vacation is $100. A random sample of 20 such groups of adults has a mean daily meal cost of $95 and a standard deviation of $4.50. Is there enough evidence to reject the claim at a = 0.1? complete parts A – D.T =
      P Value =
    1. Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion p at the given level of significance a using given sample statistics.
      Claim p = a = sample statistics: p = n =Can the normal sampling distribution be used?
      Answer:

The critical values are =
z =
What is the result of the test?
Answer:

18 Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion p at the given level of significance a using given sample statistics.
Claim p = 0.23, a = 0.10, sample statistics: p = 0.18, n = 150.
Can the normal sampling distribution be used?

    1. (a) write the claim mathematically and identify Ho and Ha. (b) find the critical value(s) and identify the rejection region(s). find the standardized test statistic. (d) decide whether to reject or fail to reject the null hypothesis. An environmental agency recently claimed more than 25% of consumers have stopped buying a certain product because of environmental concerns. In a random sample of 1000 customers, you find 40% have stopped buying the product. At a=0.03, do you have enough evidence to support the claim?

Zo = 1.88
Z =

19 (a) write the claim mathematically and identify Ho and Ha. (b) find the critical value(s) and identify the rejection region(s). find the standardized test statistic. (d) decide whether to reject or fail to reject the null hypothesis. An environmental agency recently claimed more than 25% of consumers have stopped buying a certain product because of environmental concerns. In a random sample of 1000 customers, you find 40% have stopped buying the product. At a=0.03, do you have enough evidence to support the claim?

  1.  A humane society claims that less than 36% of U.S. households own a dog. In a random sample of 406 U.S. households, 154 say they own a dog. At a = 0.10, is there enough evidence to support the society’s claim?
    (a) write the claim mathematically and identify Ho and Ha. (b) find the critical value(s) and identify the rejection region(s). (c) find the standardized test statistic. (d) decide whether to reject or fail to reject the null hypothesis, and € interpret the decision in the context of the original claim.

Critical Values =

A =

Statistics for Decision Making

Discussions Recent Week 1-7 All Posts 332 Pages 

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Descriptive Statistics Discussions Week 1 All Post 50 Pages

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If you were given a large data set, such as the sales over the last year of our top 100 customers, what might you be able to do with these data? What might be the benefits of describing the data?  Anyone, can you identify the level of measurement of the data corresponding to a particular variable? Is it quantitative data or qualitative data? How might you organize or summarize the data?  What is an example of a variable that has ratio measure?  How might you describe or summarize the data for this variable?  How do we determine the mean and the median for a set of data?  When might it be preferable to use the median as the measure of center rather than the mean?…

Regression Discussions Week 2 All Posts 45 Pages

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Suppose you are given data from a survey showing the IQ of each person interviewed and the IQ of his or her mother. That is all the information that you have. Your boss has asked you to put together a report showing the relationship between these two variables. What could you present and why?  Assume that you have ordered pairs of data (x, y) representing the IQ of the mother and the IQ of the interviewee. How might you investigate the relationship between these two variables?  If we were to collect data and create a scatter plot, what information could we obtain about the correlation by looking at the scatter plot?  Hint:  look at the scatter plots on page 470 in your textbook. How can we obtain a measure of the strength and direction of the linear correlation based on the data?…

Probability and Odds Discussions Week 3 All Posts 51 Pages

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The odds of winning a game are given as 1:10. What is the probability that you will win this game? What is the probability that you will lose this game? In your follow up replies, consider which number in the odds ratio needs to change and how in order to increase the probability of winning. Give this problem a try: If the odds of winning are 5:12, what is the probability of winning?  What is the probability that on a single toss of a nickel and a dime, what is the probability that both the nickel and dime land on heads?

Suppose you have to select a four-digit PIN number and all four digits must be different.  How many different PIN numbers are possible?  Suppose someone tries to guess your PIN number. What is the probability that the person will guess your PIN number on the first try?  Write your answer as a fraction. STANDARD DECK OF CARDS:  Suppose you randomly select one card from a standard 52-card deck.  What is the probability that the card will be a King?  What is the probability that the card will be a seven or a nine?  What is the probability that the card will be a King or a heart?  Include explanations with your answers…

Discrete Probability Variables Discussions Week 4 All Post 53 Pages

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 Provide an example that follows either the binomial or Poisson distribution, and explain why that example follows that particular distribution. In your responses to other students, make up numbers for the example provided by that other student, and ask a related probability question. Then show the work (or describe the technology steps) and solve that probability example.  Use technology to find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Briefly explain how you obtained your answers.  In a typical day, 61% of U.S. adults go online to get news. You randomly select ten U.S. adults. Find the probability that the number of U.S. adults in your sample who say they go online to get news is (a) exactly five, (b) at least six, (c) less than four.  Please include explanations with your answers. For example, which type of probability distribution did you use to solve the problem? How did you use technology to solve each part of the problem?  Use technology to find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Briefly explain how you obtained your answers.

The mean number of oil tankers at a port city is eight per day. Find the probability that the number of oil tankers on any given day is (a) exactly eight, (b) at most four, (c) more than eight.  Use technology to find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Briefly explain how you obtained your answers.

 The probability that a student passes the written test for a private pilot license is 0.75. Find the probability that the student (a) passes on the first attempt, (b) passes on the second attempt, (c) passes on the first or second attempt, (d) does not pass on the first or second attempt….

Statistics for Decision Making

 Interpreting Normal Distributions Discussions Week 5 All Posts 46 Pages

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Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. What percent of the measurements would we expect to be 115 or more?  Explain your solution.  Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Suppose a sample of size 5 was randomly selected from this population. Would it be unusual for the sample mean to be 115 or more? Why or why not?  Solve the following problem. Round each answer to the nearest whole number.

Briefly explain to your classmates how you obtained your solution. Give an interpretation for each answer. HEART TRANSPLANT WAITING TIMES  (adapted from p. 258 problem #33 in our textbook)The time spent (in days) waiting for a heart transplant for people ages 35-49 can be approximated by a normal distribution with mean = 203 days and standard deviation = 25.7 days. a) What waiting time represents the 10th percentile?  b) What waiting time represents the first quartile?  A machine is set to fill milk containers with a mean of 64 ounces and a standard deviation of 0.11 ounce.  A random sample of 40 containers has a mean of 64.05 ounces. Does the machine need to be reset? Explain….

Confidence Interval Concepts Discussions Week 6 All Posts 45 Pages

Consider the formula used for any confidence interval and the elements included in that formula. What happens to the confidence interval if you (a) increase the confidence level, (b) increase the sample size, or (c) increase the margin of error? Only consider one of these changes at a time. Explain your answer with words and by referencing the formula.  In a random sample of 24 people, the mean body mass index (BMI) was 27.7 and the standard deviation was 6.12. Use the t-distribution to construct a 99% confidence interval for the population mean BMI. Round your answer to one decimal place as needed. Explain how you solved this problem. I encourage you to use technology! Give an interpretation for your answer.

Suppose you wish to estimate with 90% confidence, the population proportion of U.S. adults who think that foods containing genetically modified ingredients should be labeled. Your estimate must be within 3% of the population proportion. a)   Find the minimum sample size needed, if no preliminary estimate is available. b)   Find the minimum sample size needed, using results from a prior study that found that 87% of U.S. adults think that foods containing genetically modified foods should be labeled. c)    Compare your answers for parts (a) and (b). Include an explanation regarding how you determined your sample sizes…

Hypothesis Testing Discussions Week 7 All Posts 42 Pages

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Why do you think statisticians are asked to complete hypothesis testing? Can you find or think of examples in courts, in medicine, or in your field? What is the meaning of the P-value in a hypothesis test?  When do you reject or fail to reject the null hypothesis?  Choose a statement below. Write the null and alternative hypotheses in symbolic form. Identify which hypothesis is the claim. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

  1. a)       A light bulb manufacturer claims that the mean life of a certain type of light bulb is more than 750 hours.
  2. b)       A consumer group claims that the mean annual consumption of coffee by a person in the United States is 23.2 gallons.
  3. c)       A report claims that 87% of lung cancer deaths are due to tobacco use.
  4. d)       A baseball team claims that the mean length of its games is less than 2.5 hours.
  5. e)       A resort claims that more than half of all customers return for another visit.

A credit card company claims that the mean credit card debt for individuals is greater than $5000. You want to test the claim. You find that a random sample of 28 cardholders has a mean credit card balance of $5160 and a standard deviation of $610.  At alpha = 0.05, is there sufficient evidence to support the claim? Perform a t-test for the mean. Use the following 5 steps, and include explanations. You may also choose to elaborate on a classmate’s response.

1)   State the null and alternative hypotheses. Identify which statement is the claim.

2)   Determine the value of the standardized test statistic, t. (Round to 2 decimal places as needed.)

3)   Find the P-value. (Round to 3 decimal places as needed.)

4)   Decide whether to reject or fail to reject the null hypothesis.

5)   Interpret the decision in the context of the original claim…

Statistics for Decision Making

Final Exam 

https://www.hiqualitytutorials.com/product/math-221-final-exam/

  1. The list of books that your friend reads for school for the past five months is shown below:

Private London

Spring Fever

Kiss The Dead

Threat Vector

The Racketeer

Question: What is the data set’s level of measurement? Explain your reasoning.

  1. 2. Identify the sampling techniques used, and discuss potential sources of bias (if any). Choose at random, 430 customers at an electronics store are contacted and asked their opinions of the services they received.
    Question: what type of sampling is used?
    Question: what potential sources of bias are present, if any? Select all that supply.
  2. 3. Match the plot with a possible description of the sample.
  3. 4. The number of credits being taken by a sample of 13 full-time college students are listed below. find the mean, median, and mode of the data, if possible. if any measure cannot be found or does not represent the center of the data, explain why.
    5 5 8 8 5 4 4 4 6 4 4 4 7
    Find the mean. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Does the mean represent the center of the data?

Does the median represent the center of the data?

Find the mode.  Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Does (Do) the mode(s) represent the center of the data?

  1. 5. The ages of 10 brides at their first marriage are given below. Complete parts (a) and (b) below.
    3 41.3 25.4 41.2 45.6 30.1 22.5 35.3 28.1 37.8

Find the range of the data set:

Change 45.6 to 61.2 and find the range of the new data set.

  1. 6. The mean value of land and buildings per acre from a sample of farms is $1300, with a standard deviation of $200. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 80.

Question: Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1100 and $1500
Question: If 23 farms were sampled, about how many of these additional farms would you expect to have land and building values between $1100 – $1500 per acre?

  1. 7. The table below shows the results of a survey in which 141 men and 144 women workers ages 25 to 64 were asked if they have at least one month’s income set aside for emergencies. Complete parts (a) through (d)

Question: Find the probability that a randomly selected worker has one month’s income or more set aside for emergencies.
Question: Given that a randomly selected worker is a male, find the probability that the worker has less than one month’s  income:
Question: Given that a randomly selected worker has one month’s income or more, find the probability that the worker is a female.
Question: Are the events having less than one month’s income saved and being male independent or dependent?

  1. 8. The probability that a person in the United States has type B* Blood is 11%. Five unrelated people in the US are selected at random. Complete parts (a) through (d).

Question: What is the probability that none of the five have type B* Blood?
Question: What is the probability at least one person has type B* Blood?
Question: Which of the events can be considered unusual?

  1. 9. The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts (a) through (d)

Question: Find the probability that the student is male or a nursing major.
Question: Find the probability that the student is female or not a nursing major
Question: Find the probability that the student is not female or a nursing major:
Question: Are the events being male and being a nursing major mutually exclusive?

  1. 10. Evaluate the given expression and express the results using the usual format for writing numbers (instead of scientific notation). 47P2  11. Outside a home, there is a 6-key keypad with the letters A, B , C ,D ,E , and F that can be used to open the garage if the correct six letter code is entered. Each key may be used only once. How many codes are possible.
    Answer: The possible number of codes is…
  2. 12. A frequency distribtion is shown below. complete parts (a) through (b)
    The number of televisions per household in a small town:

Televisions 0 1 2 3
Households 29 448 729 1400

X         P(x)
0          0.011
1          0.172
2          0.280
3          0.537

Describe the histogram’s shape. Choose the correct answer below.
13. 64% of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability that the # who consider themselves baseball fans is (a) exactly 5, (b) at least 6, and (c) less than hour.

A =
B=
C=

  1. 14. 37% of college students say they use credit cards because of the rewards program. you randomly select 10 college students and ask each to name the reason he or she uses credit cards. find the probability that the number of college students who say they use credit cards because of the rewards program is (a) exactly two, (b) more than two, or (c) between two and five.

A=
B=
C =

  1. Given that x has a Possion distribution with u = 1.8, what is the probability that x = 2
    P(2) =
  2. 16. The mean incubation time for a type of fertilized egg kept at 100.4 F is 20 days. Suppose that the incubation times are approimately normally distrubted with a standard deviation of 2 days.
    A: What is the probability that a randomly selected egg hatches in less than 16 days?
    B: What is the probability that a randomly selected egg hatches between 18 and 20 days?
    C: What is the probability that a randomly selected egg takes over 24 days to hatch?

A =
B =
C =

  1. 17. Use the normal distribution of SAT critical reading scores for which the mean is 512 and the standard deviation is 125. Assume the variable X is normally distributed.
    A: What percent of SAt verbal scores are less than 600?
    B: If 1000 SAT scores are randomly selected, how many would be greater than 575?

A =
B =

  1. 18. The time spent in days waiting for a heart transplant for people ages 35-49 can be approximately by the normal distribution, as shown in the figure to the right.
  1. A) what waiting time represents the 5th percentile?
    B) what waiting time represents the 3rd quartile?

A =

B =

  1. 19. Find the probability and interpret the results. If convenient, use technology to find the probability.

The population mean annual salary for environmental compliance specialists is about $60,500. A random sample of 40 specialists is drawn from this population. what is the probability that the mean salary of the sampel is less than $57,00? Assume a = $5,500.

  1. 20. Construct the confidence interval for the population mean u.
    C = 0.98, x = 8.8, o = 0.6, n = 60
  2. 21. A machine cuts plastic into sheets that are 45 feet long. Assume the population of lengths is normally distributed. Complete parts (a) and (b)

N =
N =
the tolerance of E =

  1. 22. Construct the indicated confidence interval for the population mean u using t-distribution
    c = .99, x = 111, s = 10, n = 9
    23. In a survey of 4092 adults, 714 say they have seen a ghost. Construct a 99% confidence interval for the population proportion. Interpret the results.
  2. 24. A researcher wishes to estimate, with 99% confidence, the population proportion of adults who are confident with their country’s banking system. His estimate must be accurate within 4% of the population proportion.

A =
B =
C = Having an estimate of the population proportion…

  1. 25. For the statement below, write the claim as a mathemetical statement. State the null and alternative hypotheses and identify which represents the claim. A company claims that it’s brands of paint have a mean drying time of more than 20 minutes.
  2. 26. The lengths of time (in years) it took a random sample of 32 former smokers to quit smoking is permanently listed. assume the population standard deviation is 4.1 years. At a = 0.05, is there enough evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 years?
  1. 27. Use a t-test to test the claim about the population mean u at the given level of significance using the given sample statistics. Assume the population is normally distributed.
    Claim u = 28, a = 0.05. Sample statistics x = 23.7, s = 4.6, n = 14
    28. An annual survey of first-year college students asks 277,000 students about their attitudes on a variety of subjects, According to a recent survey, 58% of first-year students believe that the abortion should be legal. Use a 0.05 significance level to test the claim that over half of all first year students believe that abortion should be legal.

Conclusion…

  1. 29. Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (the pair of variables has a significant correlation. Then use the regression equation to predict the value of y for each of the given x values, if meaningful. The table shows the shoe size and heights for 6 men.
    Shoe size x: 7.5, 8.0, 11.00, 11.6, 12.6, 13.5
    Height y: 66.0, 70.0, 72.0, 73.0, 73.0, 73.0

A =
B =
C =

D =

  1. 30. Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variations of the data about the regression line?

Coefficient of determination:
% of the variation can be explained by the regression line.
% of the variation is unexplained and is due to other factors or to sampling error.

  1. 31. The equation used to predict the total body weight (in pounds) of a female athlete at a certain school is y = -118 + 3.44x + 2.11x where x is the female athlete’s height in inches and x2 is the females body fat % measured as X2%. Use the multiple regression equation to predict the total body weight for a female athlete who is 67 inches tall and has 15% body fat.

Statistics for Decision Making

Final Exam Set 2

https://www.hiqualitytutorials.com/product/math221-final-exam-statistics/

  1. The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts (a) through (d) (a)Find the probability that the student is male or a nursing major.

P (being male or being nursing major) =
(b) Find the probability that the student is female or not a nursing major.
P(being female or not being a nursing major) =
(c) Find the probability that the student is not female or a nursing major
P(not being female or not being a nursing major) =
(d) Are the events “being male” and “being a nursing major” mutually exclusive? Explain.

  1. An employment information service claims the mean annual pay for full-time male workers over age 25 without a high school diploma is $22,325. The annual pay for a random sample of 10 full-time male workers over age 25 without a high school diploma is listed. At a = 0.10, test the claim that the mean salary is $22,325. Assume the population is normally distributed.

20,660 – 21,134 – 22,359 – 21,398 – 22,974, – 16,919 – 19,152 – 23,193 – 24,181 – 26,281

(a) Write the claim mathematically and identify

Which of the following correctly states ?

(b) Find the critical value(s) and identify the rejection region(s).

What are the critical values?

Which of the following graphs best depicts the rejection region for this problem?

(c) Find the standardized test statistics.
t =

(d) Decide whether to reject or fail to reject the null hypothesis.
reject because the test statistics is in the rejection region.

  1. fail to reject because the test statistic is not in the rejection region.
    c. reject because the test statistic is not in the rejection region.
    d. fail to reject  because the test statistic is in the rejection region.

(e) Interpret the decision in the context of the original claim.
a. there is sufficient evidence to reject the claim that the mean salary is $22,325.
b. there is not sufficient evidence to reject the claim that the mean salary is not $22,325.
c. there is sufficient evidence to reject the claim that the mean salary is not $22,325.
d. there is not sufficient evidence to reject the claim that the mean salary is $22,325.

  1. The times per week a student uses a lab computer are normally distributed, with a mean of 6.1 hours and a standard deviation of 1.2 hours. A student is randomly selected. Find the following probabilities.
    (a) The probability that the student uses a lab computer less than 5hrs a week.
    (b) The probability that the student uses a lab computer between 6-8 hrs a week.

(c) The probability that the student uses a lab computer for more than 9 hrs a week.

(a) =
(b) =
(c) =

  1. Write the null and alternative hypotheses. Identify which is the claim.
    A study claims that the mean survival time for certain cancer patients treated immediately with chemo and radiation is 13 months.
  2. Find the indicated probability using the standard normal distribution.
    P(z>) =
  3. The Gallup Organization contacts 1323 men who are 40-60 years of age and live in the US and asks whether or not they have seen their family doctor.What is the population in the study?
    Answer:What is the sample in the study?
    Answer:
  1. The ages of 10 brides at their first marriage are given below.
    4 32.2     33.6     41.2     43.4     37.1     22.7     29.9     30.6     30.8(a) find the range of the data set.
    Range =
    (b) change 43.4 to 58.6 and find the range of the new date set.
    Range =
    (c) compare your answer to part (a) with your answer to part (b)
  1. The following appear on a physician’s intake form. Identify the level of measurement of the data.
    (a) Martial Status
    (b) Pain Level (0-10)
    (c) Year of Birth
    (d) Height(a) what is the level of measurement for marital status(b) what is the level of measurement for pain level(c) what is the level of measurement for year of birthWhat is the level of measurement for height
  1. To determine her air quality, Miranda divides up her day into 3 parts; morning, afternoon, and evening. She then measures her air quality at 3 randomly selected times during each part of the day. What type of sampling is used?
  1. Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below.
  • X= 150 calories
  • X= 100 calories
  • X = 120 calories
  • X = 60 calories

Find the regression equation.
=
Choose the correct graph below.

(a) predict the value of y for x = 150.
Answer:
(b) predict the value of y for x = 100.
Answer:
(c) predict the value of y for x = 120.
Answer:
(d) predict the value of y for x = 60.
Answer:

  1.  A restaurant association says the typical household spends a mean of $4072 per year on food away from home. You are a consumer reporter for a national publication and want to test this claim. You randomly select 12 households and find out how much each spent on food away from home per year. Can you reject the restaurant association’s claim at a = 0.10? Complete parts a through d.
  • Write the claim mathematically and identify. Choose the correct the answer below.

Use technology to find the P-value.
P =
Decide whether to reject or fail the null hypothesis.

Interpret the decision in the context of the original claim. Assume the population is normally distributed. Choose the correct answer below.

  1.  The table below shows the results of a survey in which 147 families were asked if they own a computer and if they will be taking a summer vacation this year.

(a) find the probability that a randomly selected family is not taking a summer vacation year.
Probability =
(b) find the probability that a randomly selected family owns a computer
Probability =
(c) find the probability that a randomly selected family is taking a summer vacation this year and owns a computer
Probability =
(d) find the probability a randomly selected family is taking a summer vacation this year and owns a computer.
Probability =

  • Are the events of owning a computer and taking a summer vacation this year independent or dependent events?
  • 13. Assume the Poisson distribution applies. Use the given mean to find the indicated probability.
    Find P(5) when ᶙ = 4

P(5) =

  1.  In a survey of 7000 women, 4431 say they change their nail polish once a week. Construct a 99% confidence interval for the population proportion of women who change their nail polish once a week.
    A 99% confidence interval for the population proportion is…

15 A random sample of 53 200-meter swims has a mean time of 3.32 minutes and the population standard deviation is 0.06 minutes. Construct a 90% confidence interval for the population mean time. Interpret the results.
The 90% confidence interval is

Interpret these results. Choose the correct answer:
Answer: With 90% confidence, it can be said that the population mean time is between the end points of the given confidence interval.

  1. Determine whether the variable is qualitative or quantitative: Weight

Quantitative
Qualitative

  1. 32% of college students say that they use credit cards because of the reward program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of college students who say they use credit cards because of the reward program is (a) exactly two, (b), more than two, and (c), between two and five inclusive.

(a) P(2) =
(b) P(X>2) =
(c) P(2<x<5) =

  1.  A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 950 hours. A random sample of 74 light bulbs has a mean life of 943 hours with a standard deviation of 90 hours. Do you have enough evidence to reject the manufacturer’s claim? Use ᶏ = 0.04
  • Identify the critical value(s).(c) identify the standardized test statistic.
    z =
    (d) decide whether to reject or fail to reject the null hypothesis.A. Reject . There is sufficient evidence to reject the claim that the bulb life is at least 950 hours.
    B. Fail to reject . There is not sufficient evidence to reject the claim that the mean bulb life is at least 950 hours.
    C. Fail to reject . There is sufficient evidence to reject the claim that mean bulb life is at least 950 hours.
    D. Reject . There is not sufficient evidence to reject the claim that mean bulb life is at least 950 hours.19. Use technology to find the sample size, mean, medium, minimum data value, and maximum data value of the data. The data represents the amount (in dollars) made by several families during a community yard sale.
    25 67.25 156      134.75 98.25   149.25 124.75 109.75 117      104.75 76The sample size is
    The mean is
    The medium is
    The minimum data value is
    The maximum data value is20. A researcher wishes to estimate, with 95% confidence, the proportion of adults who have high-speed internet access. Her estimate must be accurate within 5% of the true proportion.
    (a) find the minimum sample size needed, using a prior study that found 54% of the respondents said they have high-speed internet access.
    (b) no preliminary estimate is available. Find the minimum sample size needed.(a) what is the minimum sample size needed using a prior study that found that 54% of the respondents said they have high-speed internet access?n =(b) what is the minimum sample size needed assuming that no preliminary estimate is available?n =21. You interview a random sample of 50 adults. The results of the survey show that 50% of the adults said they were more likely to buy a product where there are free samples. At ᶏ = 0.05, can you reject the claim that at least 54% of the adults are more likely to buy a product when there are free samples?State the null and alternative hypotheses. Choose the correct answer below.

Determine the critical value(s).

The critical value(s) is/are

find the z-test statistic.
z =

what is the result of the test?
A. reject . The data provide sufficient evidence to reject the claim.

  1. fail to reject . The data provide sufficient evidence to reject the claim.
    C. Reject . The data do not provide sufficient evidence to reject the claim.
    D. fail to reject . The data do not provide sufficient evidence to reject the claim.
  1.  The budget (in millions of dollars) and worldwide gross (in millions of dollars) for eight movies are shown below. Complete parts (a) through (c)
Budget X209203198198179176175168
Gross Y254341453656721104918391267

(a) display the data in a scatter plot. Choose the correct graph below.

(b) calculate the correlation coefficient r.
r =

(c) make a conclusion about the type of correlation.
The correlation is a …linear correlation.

  1.  A machine cuts plastic into sheets that are 30 feet (360 inches) long. Assume that the population of lengths is normally distributed. Complete parts a and b.
  • The company wants to estimate the mean length the machine is cutting the plastic within 0.125 inch. Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 0.25 inch.
    n =
    Repeat part (a) using an error tolerance of 0.0625 inch.
    n =

Which error tolerance requires a larger sample size? Explain.

  1.  The tolerance E = 0.0625 inch requires a larger sample size. As error size decreases, a larger sample must be taken to ensure the desired accuracy.
    B.  The tolerance E = 0.125 inch requires a larger sample size. As error size decreases, a larger sample must be taken to ensure the desired accuracy.
    C.  The tolerance E = 0.125 inch requires a larger sample size. As error size increases, a larger sample must be taken to ensure the desired accuracy.
    D.  The tolerance E = 0.0.625 inch requires a larger sample size. As error size increases, a larger sample must be taken to ensure the desired accuracy.

Statistics for Decision Making

DeVry